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Authors:
(1) Scott Conn, California Institute of Technology, Pasadena, California;
(2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California;
(3) Jorn Callies, California Institute of Technology, Pasadena, California. Table of Links Abstract and Intro Observations Models Results Discussion Conclusion APPENDIX A APPENDIX B APPENDIX C References References Alford, M. H., 2001: Internal swell generation: The spatial distribution of energy flux from the wind to mixed layer near-inertial motions. Journal of Physical Oceanography, 31 (8), 2359–2368. Alford, M. H., 2020: Revisiting near-inertial wind work: Slab models, relative stress, and mixed layer deepening. Journal of Physical Oceanography, 50 (11), 3141–3156. Alford, M. H., J. A. MacKinnon, H. L. Simmons, and J. D. Nash, 2016: Near-inertial internal gravity waves in the ocean. Annual review of marine science, 8, 95–123. Arbic, B. K., and G. R. Flierl, 2004: Baroclinically unstable geostrophic turbulence in the limits of strong and weak bottom ekman friction: Application to midocean eddies. Journal of Physical Oceanography, 34 (10), 2257–2273. Asselin, O., and W. R. Young, 2020: Penetration of wind-generated near-inertial waves into a turbulent ocean. Journal of Physical Oceanography, 50 (6), 1699–1716. Balmforth, N., S. G. Llewellyn Smith, and W. Young, 1998: Enhanced dispersion of near-inertial waves in an idealized geostrophic flow. Journal of marine research, 56 (1), 1–40. Balmforth, N. J., and W. R. Young, 1999: Radiative damping of near-inertial oscillations in the mixed layer. Journal of marine research, 57 (4), 561–584. Buckingham, C. E., and Coauthors, 2016: Seasonality of submesoscale flows in the ocean surface boundary layer. Geophysical Research Letters, 43 (5), 2118–2126. Burns, K. J., G. M. Vasil, J. S. Oishi, D. Lecoanet, and B. P. Brown, 2020: Dedalus: A flexible framework for numerical simulations with spectral methods. Phys. Rev. Res., 2, 023 068. Callies, J., R. Barkan, and A. N. Garabato, 2020: Time scales of submesoscale flow inferred from a mooring array. Journal of Physical Oceanography, 50 (4), 1065–1086. Damerell, G. M., K. J. Heywood, D. Calvert, A. L. Grant, M. J. Bell, and S. E. Belcher, 2020: A comparison of five surface mixed layer models with a year of observations in the north atlantic. Progress in Oceanography, 187, 102 316. Damerell, G. M., K. J. Heywood, A. F. Thompson, U. Binetti, and J. Kaiser, 2016: The vertical structure of upper ocean variability at the porcupine abyssal plain during 2012–2013. Journal of Geophysical Research: Oceans, 121 (5), 3075–3089. D’Asaro, E. A., 1985: The energy flux from the wind to near-inertial motions in the surface mixed layer. Journal of Physical Oceanography, 15 (8), 1043–1059. D’Asaro, E. A., 1995: Upper-ocean inertial currents forced by a strong storm. Part III: Interaction of inertial currents and mesoscale eddies. Journal of physical oceanography, 25 (11), 2953–2958. D’Asaro, E. A., C. C. Eriksen, M. D. Levine, P. Niiler, P. Van Meurs, and Coauthors, 1995: Upperocean inertial currents forced by a strong storm. Part I: Data and comparisons with linear theory. Journal of Physical Oceanography, 25 (11), 2909–2936. Dewar, W. K., and G. R. Flierl, 1987: Some effects of the wind on rings. Journal of Physical Oceanography, 17 (10), 1653–1667. Essink, S., E. Kunze, R.-C. Lien, R. Inoue, and S.-i. Ito, 2022: Near-inertial wave interactions and turbulence production in a kuroshio anticyclonic eddy. Journal of Physical Oceanography, 52 (11), 2687–2704. Ferrari, R., and C. Wunsch, 2009: Ocean circulation kinetic energy: Reservoirs, sources, and sinks. Annual Review of Fluid Mechanics, 41, 253–282. Flexas, M. M., A. F. Thompson, H. S. Torres, P. Klein, J. T. Farrar, H. Zhang, and D. Menemenlis, 2019: Global estimates of the energy transfer from the wind to the ocean, with emphasis on near-inertial oscillations. Journal of Geophysical Research: Oceans, 124 (8), 5723–5746. Gill, A. E., 1984: On the behavior of internal waves in the wakes of storms. Journal of Physical Oceanography, 14 (7), 1129–1151. Gnanadesikan, A., M.-A. Pradal, and R. Abernathey, 2015: Isopycnal mixing by mesoscale eddies significantly impacts oceanic anthropogenic carbon uptake. Geophysical Research Letters, 42 (11), 4249–4255. Guan, S., W. Zhao, J. Huthnance, J. Tian, and J. Wang, 2014: Observed upper ocean response to typhoon megi (2010) in the northern south china sea. Journal of Geophysical Research: Oceans, 119 (5), 3134–3157. Hersbach, H., and Coauthors, 2018: Era5 hourly data on single levels from 1979 to present. Copernicus climate change service (c3s) climate data store (cds), 10 (10.24381). Jayne, S. R., and J. Marotzke, 2002: The oceanic eddy heat transport. Journal of Physical Oceanography, 32 (12), 3328–3345. Jochum, M., B. P. Briegleb, G. Danabasoglu, W. G. Large, N. J. Norton, S. R. Jayne, M. H. Alford, and F. O. Bryan, 2013: The impact of oceanic near-inertial waves on climate. Journal of Climate, 26 (9), 2833–2844. Kato, H., and O. Phillips, 1969: On the penetration of a turbulent layer into stratified fluid. Journal of Fluid Mechanics, 37 (4), 643–655. Kunze, E., 1985: Near-inertial wave propagation in geostrophic shear. Journal of Physical Oceanography, 15 (5), 544–565. Large, W., and S. Pond, 1981: Open ocean momentum flux measurements in moderate to strong winds. Journal of physical oceanography, 11 (3), 324–336. Lee, D.-K., and P. P. Niiler, 1998: The inertial chimney: The near-inertial energy drainage from the ocean surface to the deep layer. 103 (C4), 7579–7591. Moehlis, J., and S. G. L. Smith, 2001: Radiation of mixed layer near-inertial oscillations into the ocean interior. Journal of physical oceanography, 31 (6), 1550–1560. M¨uller, P., J. McWilliams, and J. Molemaker, 2011: Routes to dissipation in the ocean: The 2D/3D turbulence conundrum. Marine Turbulence: Theories, Observations, and Models, Cambridge University Press. Nikurashin, M., G. K. Vallis, and A. Adcroft, 2013: Routes to energy dissipation for geostrophic flows in the Southern Ocean. Nature Geoscience, 6 (1), 48–51. Plueddemann, A., and J. Farrar, 2006: Observations and models of the energy flux from the wind to mixed-layer inertial currents. Deep Sea Research Part II: Topical Studies in Oceanography, 53 (1-2), 5–30. Pollard, R. T., and R. Millard, 1970: Comparison between observed and simulated wind-generated inertial oscillations. Deep Sea Research and Oceanographic Abstracts, 17, 813–821. Pollard, R. T., P. B. Rhines, and R. O. Thompson, 1973: The deepening of the wind-mixed layer. Geophysical Fluid Dynamics, 4 (4), 381–404. Rama, J., C. J. Shakespeare, and A. M. Hogg, 2022: The wavelength dependence of the propagation of near-inertial internal waves. Journal of Physical Oceanography, 52 (10), 2493–2514. Renault, L., M. J. Molemaker, J. C. McWilliams, A. F. Shchepetkin, F. Lemarie, D. Chelton, ´ S. Illig, and A. Hall, 2016: Modulation of wind work by oceanic current interaction with the atmosphere. Journal of Physical Oceanography, 46 (6), 1685–1704. Rocha, C. B., G. L. Wagner, and W. R. Young, 2018: Stimulated generation: extraction of energy from balanced flow by near-inertial waves. Journal of Fluid Mechanics, 847, 417–451. Taburet, G., A. Sanchez-Roman, M. Ballarotta, M.-I. Pujol, J.-F. Legeais, F. Fournier, Y. Faugere, and G. Dibarboure, 2019: Duacs dt2018: 25 years of reprocessed sea level altimetry products. Ocean Science, 15 (5), 1207–1224. Thomas, L. N., L. Rainville, O. Asselin, W. R. Young, J. Girton, C. B. Whalen, L. Centurioni, and V. Hormann, 2020: Direct observations of near-inertial wave 𝜁-refraction in a dipole vortex. Geophysical Research Letters, 47 (21), e2020GL090 375. Thompson, A. F., A. Lazar, C. Buckingham, A. C. N. Garabato, G. M. Damerell, and K. J. Heywood, 2016: Open-ocean submesoscale motions: A full seasonal cycle of mixed layer instabilities from gliders. Journal of Physical Oceanography, 46 (4), 1285–1307. von Storch, J.-S., and V. L¨uschow, 2023: Wind power input to ocean near-inertial waves diagnosed from a 5-km global coupled atmosphere-ocean general circulation model. Journal of Geophysical Research: Oceans, 128 (2), e2022JC019 111. Wagner, G., and W. Young, 2016: A three-component model for the coupled evolution of near-inertial waves, quasi-geostrophic flow and the near-inertial second harmonic. Journal of Fluid Mechanics, 802, 806–837. Wunsch, C., and R. Ferrari, 2004: Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech., 36, 281–314. Xie, J.-H., and J. Vanneste, 2015: A generalised-lagrangian-mean model of the interactions between near-inertial waves and mean flow. Journal of Fluid Mechanics, 774, 143–169. Young, W., and M. Ben Jelloul, 1997: Propagation of near-inertial oscillations through a geostrophic flow. JMR, 55, 735–766. Yu, X., A. C. Naveira Garabato, C. Vic, J. Gula, A. C. Savage, J. Wang, A. F. Waterhouse, and J. A. MacKinnon, 2022: Observed equatorward propagation and chimney effect of near-inertial waves in the midlatitude ocean. Geophysical Research Letters, 49 (13), e2022GL098 522. Zhai, X., H. L. Johnson, and D. P. Marshall, 2010: Significant sink of ocean-eddy energy near western boundaries. Nature Geoscience, 3 (9), 608–612. This paper is available on arxiv under CC 4.0 license. Authors: (1) Scott Conn, California Institute of Technology, Pasadena, California; (2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California; (3) Jorn Callies, California Institute of Technology, Pasadena, California. Authors: Authors: (1) Scott Conn, California Institute of Technology, Pasadena, California; (2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California; (3) Jorn Callies, California Institute of Technology, Pasadena, California. Table of Links Abstract and Intro Abstract and Intro Observations Observations Models Models Results Results Discussion Discussion Conclusion Conclusion APPENDIX A APPENDIX A APPENDIX B APPENDIX B APPENDIX C APPENDIX C References References References Alford, M. H., 2001: Internal swell generation: The spatial distribution of energy flux from the wind to mixed layer near-inertial motions. Journal of Physical Oceanography, 31 (8), 2359–2368. Alford, M. H., 2020: Revisiting near-inertial wind work: Slab models, relative stress, and mixed layer deepening. Journal of Physical Oceanography, 50 (11), 3141–3156. Alford, M. H., J. A. MacKinnon, H. L. Simmons, and J. D. Nash, 2016: Near-inertial internal gravity waves in the ocean. Annual review of marine science, 8, 95–123. Arbic, B. K., and G. R. Flierl, 2004: Baroclinically unstable geostrophic turbulence in the limits of strong and weak bottom ekman friction: Application to midocean eddies. Journal of Physical Oceanography, 34 (10), 2257–2273. Asselin, O., and W. R. Young, 2020: Penetration of wind-generated near-inertial waves into a turbulent ocean. Journal of Physical Oceanography, 50 (6), 1699–1716. Balmforth, N., S. G. Llewellyn Smith, and W. Young, 1998: Enhanced dispersion of near-inertial waves in an idealized geostrophic flow. Journal of marine research, 56 (1), 1–40. Balmforth, N. J., and W. R. Young, 1999: Radiative damping of near-inertial oscillations in the mixed layer. Journal of marine research, 57 (4), 561–584. Buckingham, C. E., and Coauthors, 2016: Seasonality of submesoscale flows in the ocean surface boundary layer. Geophysical Research Letters, 43 (5), 2118–2126. Burns, K. J., G. M. Vasil, J. S. Oishi, D. Lecoanet, and B. P. Brown, 2020: Dedalus: A flexible framework for numerical simulations with spectral methods. Phys. Rev. Res., 2, 023 068. Callies, J., R. Barkan, and A. N. Garabato, 2020: Time scales of submesoscale flow inferred from a mooring array. Journal of Physical Oceanography, 50 (4), 1065–1086. Damerell, G. M., K. J. Heywood, D. Calvert, A. L. Grant, M. J. Bell, and S. E. Belcher, 2020: A comparison of five surface mixed layer models with a year of observations in the north atlantic. Progress in Oceanography, 187, 102 316. Damerell, G. M., K. J. Heywood, A. F. Thompson, U. Binetti, and J. Kaiser, 2016: The vertical structure of upper ocean variability at the porcupine abyssal plain during 2012–2013. Journal of Geophysical Research: Oceans, 121 (5), 3075–3089. D’Asaro, E. A., 1985: The energy flux from the wind to near-inertial motions in the surface mixed layer. Journal of Physical Oceanography, 15 (8), 1043–1059. D’Asaro, E. A., 1995: Upper-ocean inertial currents forced by a strong storm. Part III: Interaction of inertial currents and mesoscale eddies. Journal of physical oceanography, 25 (11), 2953–2958. D’Asaro, E. A., C. C. Eriksen, M. D. Levine, P. Niiler, P. Van Meurs, and Coauthors, 1995: Upperocean inertial currents forced by a strong storm. Part I: Data and comparisons with linear theory. Journal of Physical Oceanography, 25 (11), 2909–2936. Dewar, W. K., and G. R. Flierl, 1987: Some effects of the wind on rings. Journal of Physical Oceanography, 17 (10), 1653–1667. Essink, S., E. Kunze, R.-C. Lien, R. Inoue, and S.-i. Ito, 2022: Near-inertial wave interactions and turbulence production in a kuroshio anticyclonic eddy. Journal of Physical Oceanography, 52 (11), 2687–2704. Ferrari, R., and C. Wunsch, 2009: Ocean circulation kinetic energy: Reservoirs, sources, and sinks. Annual Review of Fluid Mechanics, 41, 253–282. Flexas, M. M., A. F. Thompson, H. S. Torres, P. Klein, J. T. Farrar, H. Zhang, and D. Menemenlis, 2019: Global estimates of the energy transfer from the wind to the ocean, with emphasis on near-inertial oscillations. Journal of Geophysical Research: Oceans, 124 (8), 5723–5746. Gill, A. E., 1984: On the behavior of internal waves in the wakes of storms. Journal of Physical Oceanography, 14 (7), 1129–1151. Gnanadesikan, A., M.-A. Pradal, and R. Abernathey, 2015: Isopycnal mixing by mesoscale eddies significantly impacts oceanic anthropogenic carbon uptake. Geophysical Research Letters, 42 (11), 4249–4255. Guan, S., W. Zhao, J. Huthnance, J. Tian, and J. Wang, 2014: Observed upper ocean response to typhoon megi (2010) in the northern south china sea. Journal of Geophysical Research: Oceans, 119 (5), 3134–3157. Hersbach, H., and Coauthors, 2018: Era5 hourly data on single levels from 1979 to present. Copernicus climate change service (c3s) climate data store (cds), 10 (10.24381). Jayne, S. R., and J. Marotzke, 2002: The oceanic eddy heat transport. Journal of Physical Oceanography, 32 (12), 3328–3345. Jochum, M., B. P. Briegleb, G. Danabasoglu, W. G. Large, N. J. Norton, S. R. Jayne, M. H. Alford, and F. O. Bryan, 2013: The impact of oceanic near-inertial waves on climate. Journal of Climate, 26 (9), 2833–2844. Kato, H., and O. Phillips, 1969: On the penetration of a turbulent layer into stratified fluid. Journal of Fluid Mechanics, 37 (4), 643–655. Kunze, E., 1985: Near-inertial wave propagation in geostrophic shear. Journal of Physical Oceanography, 15 (5), 544–565. Large, W., and S. Pond, 1981: Open ocean momentum flux measurements in moderate to strong winds. Journal of physical oceanography, 11 (3), 324–336. Lee, D.-K., and P. P. Niiler, 1998: The inertial chimney: The near-inertial energy drainage from the ocean surface to the deep layer. 103 (C4), 7579–7591. Moehlis, J., and S. G. L. Smith, 2001: Radiation of mixed layer near-inertial oscillations into the ocean interior. Journal of physical oceanography, 31 (6), 1550–1560. M¨uller, P., J. McWilliams, and J. Molemaker, 2011: Routes to dissipation in the ocean: The 2D/3D turbulence conundrum. Marine Turbulence: Theories, Observations, and Models, Cambridge University Press. Nikurashin, M., G. K. Vallis, and A. Adcroft, 2013: Routes to energy dissipation for geostrophic flows in the Southern Ocean. Nature Geoscience, 6 (1), 48–51. Plueddemann, A., and J. Farrar, 2006: Observations and models of the energy flux from the wind to mixed-layer inertial currents. Deep Sea Research Part II: Topical Studies in Oceanography, 53 (1-2), 5–30. Pollard, R. T., and R. Millard, 1970: Comparison between observed and simulated wind-generated inertial oscillations. Deep Sea Research and Oceanographic Abstracts, 17, 813–821. Pollard, R. T., P. B. Rhines, and R. O. Thompson, 1973: The deepening of the wind-mixed layer. Geophysical Fluid Dynamics, 4 (4), 381–404. Rama, J., C. J. Shakespeare, and A. M. Hogg, 2022: The wavelength dependence of the propagation of near-inertial internal waves. Journal of Physical Oceanography, 52 (10), 2493–2514. Renault, L., M. J. Molemaker, J. C. McWilliams, A. F. Shchepetkin, F. Lemarie, D. Chelton, ´ S. Illig, and A. Hall, 2016: Modulation of wind work by oceanic current interaction with the atmosphere. Journal of Physical Oceanography, 46 (6), 1685–1704. Rocha, C. B., G. L. Wagner, and W. R. Young, 2018: Stimulated generation: extraction of energy from balanced flow by near-inertial waves. Journal of Fluid Mechanics, 847, 417–451. Taburet, G., A. Sanchez-Roman, M. Ballarotta, M.-I. Pujol, J.-F. Legeais, F. Fournier, Y. Faugere, and G. Dibarboure, 2019: Duacs dt2018: 25 years of reprocessed sea level altimetry products. Ocean Science, 15 (5), 1207–1224. Thomas, L. N., L. Rainville, O. Asselin, W. R. Young, J. Girton, C. B. Whalen, L. Centurioni, and V. Hormann, 2020: Direct observations of near-inertial wave 𝜁-refraction in a dipole vortex. Geophysical Research Letters, 47 (21), e2020GL090 375. Thompson, A. F., A. Lazar, C. Buckingham, A. C. N. Garabato, G. M. Damerell, and K. J. Heywood, 2016: Open-ocean submesoscale motions: A full seasonal cycle of mixed layer instabilities from gliders. Journal of Physical Oceanography, 46 (4), 1285–1307. von Storch, J.-S., and V. L¨uschow, 2023: Wind power input to ocean near-inertial waves diagnosed from a 5-km global coupled atmosphere-ocean general circulation model. Journal of Geophysical Research: Oceans, 128 (2), e2022JC019 111. Wagner, G., and W. Young, 2016: A three-component model for the coupled evolution of near-inertial waves, quasi-geostrophic flow and the near-inertial second harmonic. Journal of Fluid Mechanics, 802, 806–837. Wunsch, C., and R. Ferrari, 2004: Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech., 36, 281–314. Xie, J.-H., and J. Vanneste, 2015: A generalised-lagrangian-mean model of the interactions between near-inertial waves and mean flow. Journal of Fluid Mechanics, 774, 143–169. Young, W., and M. Ben Jelloul, 1997: Propagation of near-inertial oscillations through a geostrophic flow. JMR, 55, 735–766. Yu, X., A. C. Naveira Garabato, C. Vic, J. Gula, A. C. Savage, J. Wang, A. F. Waterhouse, and J. A. MacKinnon, 2022: Observed equatorward propagation and chimney effect of near-inertial waves in the midlatitude ocean. Geophysical Research Letters, 49 (13), e2022GL098 522. Zhai, X., H. L. Johnson, and D. P. Marshall, 2010: Significant sink of ocean-eddy energy near western boundaries. Nature Geoscience, 3 (9), 608–612. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Want to Learn More About the Interactions Between Near-Inertial Waves and Mesoscale Eddies?

Authors:
(1) Scott Conn, California Institute of Technology, Pasadena, California;
(2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California;
(3) Jorn Callies, California Institute of Technology, Pasadena, California. Table of Links Abstract and Intro Observations Models Results Discussion Conclusion APPENDIX A APPENDIX B APPENDIX C References APPENDIX A YBJ kinetic energy Budget The YBJ kinetic energy budget may be formed by multiplying (2) by −𝑀∗ /2 and adding the complex conjugate. Using integration by parts, the resulting kinetic energy budget can be written as where We are free to choose C as a boundary condition on the new field 𝐴, i.e., we can choose 𝐴 at 𝑧 = −𝐻 as the solution of (A4) for some specified C. A sensible choice for the transformation is thus setting C = 0 and Under this transformation, the kinetic energy budget becomes (4), with the horizontal and vertical fluxes given by The divergence of the flux terms vanishes when the budget is integrated over the entire domain, and the only terms that can alter the domain-integrated kinetic energy are the wind work and dissipation: This paper is available on arxiv under CC 4.0 license. Authors: (1) Scott Conn, California Institute of Technology, Pasadena, California; (2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California; (3) Jorn Callies, California Institute of Technology, Pasadena, California. Authors: Authors: (1) Scott Conn, California Institute of Technology, Pasadena, California; (2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California; (3) Jorn Callies, California Institute of Technology, Pasadena, California. Table of Links Abstract and Intro Abstract and Intro Observations Observations Models Models Results Results Discussion Discussion Conclusion Conclusion APPENDIX A APPENDIX A APPENDIX B APPENDIX B APPENDIX C APPENDIX C References References APPENDIX A YBJ kinetic energy Budget The YBJ kinetic energy budget may be formed by multiplying (2) by −𝑀∗ /2 and adding the complex conjugate. Using integration by parts, the resulting kinetic energy budget can be written as where We are free to choose C as a boundary condition on the new field 𝐴, i.e., we can choose 𝐴 at 𝑧 = −𝐻 as the solution of (A4) for some specified C. A sensible choice for the transformation is thus setting C = 0 and Under this transformation, the kinetic energy budget becomes (4), with the horizontal and vertical fluxes given by The divergence of the flux terms vanishes when the budget is integrated over the entire domain, and the only terms that can alter the domain-integrated kinetic energy are the wind work and dissipation: This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

What Was the YBJ Kinectic Energy Budget In Our Near-Inertial Waves and Mesoscale Eddies Study?

Authors:
(1) Scott Conn, California Institute of Technology, Pasadena, California;
(2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California;
(3) Jorn Callies, California Institute of Technology, Pasadena, California. Table of Links Abstract and Intro Observations Models Results Discussion Conclusion APPENDIX A APPENDIX B APPENDIX C References 6. Conclusion The evolution of the NIW field at the OSMOSIS site in the Northeast Atlantic Ocean is strongly modulated by mesoscale eddies. The observed evolution can be captured by the YBJ model, which includes NIW refraction, advection, and dispersion. If these processes are omitted as in the PM model, the observations cannot be reproduced as well, even if the parameterized damping rate is tuned. The YBJ model provides a powerful interpretive framework for understanding observations of NIWs in the upper ocean. It allows us to attribute the observed evolution to specific physical processes. Lateral differences in the NIW amplitude across the mooring array are caused by 𝜁-refraction, which causes NIW kinetic energy to be fluxed into anticyclonic regions. While correlations between NIW amplitudes and mesoscale vorticity can be diagnosed from the observations alone (e.g., Yu et al. 2022), the YBJ framework produces a quantitative prediction for the NIW amplitudes that matches observations and provides a physical interpretation. The YBJ model also allows us to calculate changes in the NIW potential energy, which are expected to arise from transfers of balanced mesoscale energy (Xie and Vanneste 2015; Rocha et al. 2018). For the strongest NIW event observed during the OSMOSIS campaign, the NIW potential energy gain is at least two orders of magnitude smaller than the global average energy input into mesoscale kinetic energy. Stimulated generation therefore does not appear to have a major impact on the mesoscale eddy field in this part of the ocean. Acknowledgments. The authors thank two anonymous reviewers whose comments helped improve the presentation of this work. This material is based upon work supported by the National Science Foundation under Grant No. OCE-1924354 and by the National Aeronautics and Space Administration under Grant No. 80NSSC22K1445 issued through the Science Mission Directorate (Future Investigators in NASA Earth and Space Science and Technology). Data availability statement. The code to run the 3D YBJ model is available at https: //github.com/scott-conn/3DYBJ. All of the OSMOSIS data used as part of this study is available from the British Oceanographic Data Centre. The OSMOSIS mooring data is available at https://www.bodc.ac.uk/data/bodc_database/nodb/data_ collection/6093/. The OSMOSIS glider data is available at https://doi.org/10.5285/ 6cf0b33e-a192-549f-e053-6c86abc01204. The SSH data is available from the E.U.’s Copernicus Marine Service at https://doi.org/10.48670/moi-00148. The ERA5 reanalysis data is available from the Copernicus Climate Change Service (C3S) Climate Data Store at https: //doi.org/0.24381/cds.adbb2d47. This paper is available on arxiv under CC 4.0 license. Authors: (1) Scott Conn, California Institute of Technology, Pasadena, California; (2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California; (3) Jorn Callies, California Institute of Technology, Pasadena, California. Authors: Authors: (1) Scott Conn, California Institute of Technology, Pasadena, California; (2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California; (3) Jorn Callies, California Institute of Technology, Pasadena, California. Table of Links Abstract and Intro Abstract and Intro Observations Observations Models Models Results Results Discussion Discussion Conclusion Conclusion APPENDIX A APPENDIX A APPENDIX B APPENDIX B APPENDIX C APPENDIX C References References 6. Conclusion The evolution of the NIW field at the OSMOSIS site in the Northeast Atlantic Ocean is strongly modulated by mesoscale eddies. The observed evolution can be captured by the YBJ model, which includes NIW refraction, advection, and dispersion. If these processes are omitted as in the PM model, the observations cannot be reproduced as well, even if the parameterized damping rate is tuned. The YBJ model provides a powerful interpretive framework for understanding observations of NIWs in the upper ocean. It allows us to attribute the observed evolution to specific physical processes. Lateral differences in the NIW amplitude across the mooring array are caused by 𝜁-refraction, which causes NIW kinetic energy to be fluxed into anticyclonic regions. While correlations between NIW amplitudes and mesoscale vorticity can be diagnosed from the observations alone (e.g., Yu et al. 2022), the YBJ framework produces a quantitative prediction for the NIW amplitudes that matches observations and provides a physical interpretation. The YBJ model also allows us to calculate changes in the NIW potential energy, which are expected to arise from transfers of balanced mesoscale energy (Xie and Vanneste 2015; Rocha et al. 2018). For the strongest NIW event observed during the OSMOSIS campaign, the NIW potential energy gain is at least two orders of magnitude smaller than the global average energy input into mesoscale kinetic energy. Stimulated generation therefore does not appear to have a major impact on the mesoscale eddy field in this part of the ocean. Acknowledgments . The authors thank two anonymous reviewers whose comments helped improve the presentation of this work. This material is based upon work supported by the National Science Foundation under Grant No. OCE-1924354 and by the National Aeronautics and Space Administration under Grant No. 80NSSC22K1445 issued through the Science Mission Directorate (Future Investigators in NASA Earth and Space Science and Technology). Acknowledgments Data availability statement. The code to run the 3D YBJ model is available at https: //github.com/scott-conn/3DYBJ. All of the OSMOSIS data used as part of this study is available from the British Oceanographic Data Centre. The OSMOSIS mooring data is available at https://www.bodc.ac.uk/data/bodc_database/nodb/data_ collection/6093/. The OSMOSIS glider data is available at https://doi.org/10.5285/ 6cf0b33e-a192-549f-e053-6c86abc01204. The SSH data is available from the E.U.’s Copernicus Marine Service at https://doi.org/10.48670/moi-00148. The ERA5 reanalysis data is available from the Copernicus Climate Change Service (C3S) Climate Data Store at https: //doi.org/0.24381/cds.adbb2d47. Data availability statement. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

The End of the Ocean Trip: Concluding Our Near-Inertial Waves and Mesoscale Eddies Study

Authors:
(1) Scott Conn, California Institute of Technology, Pasadena, California;
(2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California;
(3) Jorn Callies, California Institute of Technology, Pasadena, California. Table of Links Abstract and Intro Observations Models Results Discussion Conclusion APPENDIX A APPENDIX B APPENDIX C References 5. Discussion The YBJ model does well in reproducing the mooring observations of NIWs. There are still differences between the model and the observations, however, as well as a couple of events where the YBJ model does less well. Given the observational inputs to the model, it would be surprising if this were not the case. One major limitation is the use of altimetry for the mesoscale streamfunction. As mentioned previously, the altimetry data are a heavily smoothed version of the real field. We suggested above that some of the discrepancies between the YBJ model and the observations were due to this smoothing. We also interpolated the mesoscale vorticity onto a smaller simulation grid. The resolution of the altimetry product is 0.25◦×0.25◦ , which is larger than the size of the mooring array. Differences across the mooring array come from the interpolation between neighboring altimetry grid cells, which will have introduced interpolation errors. Furthermore, we assumed that the mesoscale eddy field was barotropic. This is a reasonable assumption if the vertical scale of the waves is much smaller than the vertical scale of the eddies. There are certainly errors in the YBJ evolution, however, that arise from neglecting the baroclinicity of mesoscale eddies. These effects could be investigated in the future by running similar simulations using an in-situ data set that resolves the vertical structure of one or more eddies. In event 1, the vorticity has large variations across the mooring array (Fig. 2a). This is reflected in the NIW observations as large differences in the amplitude across the mooring array. However, this need not be the case for all events. Event 3, by contrast, shows weak variations in the vorticity (as diagnosed from altimetry) across the mooring array. The result is that the YBJ simulations also show weak variations in the NIW field across the mooring array region. The altimetry vorticity field is a heavily smoothed representation of the real vorticity field of the ocean; smaller scale vorticity features are invisible to measurements from altimetry. If there is little variation in the larger-scale vorticity across the mooring array, then these smaller-scale vorticity features may play a more important role in governing the variations in 𝜕𝑧𝑀. While we do not have a spatial map of smaller-scale vorticity features, we can estimate their magnitude at the mooring array by calculating the vorticity by applying Stokes’ theorem to the area bounded by the outer moorings (Buckingham et al. 2016). The velocity that we use in Stokes’ theorem is low-pass filtered to estimate the balanced signal. This vorticity agrees in general with the vorticity calculated from SSH but shows more high-frequency variability (Fig. 9). Event 3 shows the biggest disagreement between the two estimates of all the events. The mooring estimate shows cyclonic vorticity, whereas the altimetry estimate shows anticyclonic vorticity. This likely explains why we see the amplitude decay much quicker in observations compared to simulations because there would have been a horizontal energy flux out of the region while the simulations have a flux into the region, which acts to maintain the amplitude. The other events show better agreement between the two vorticity estimates, although there are times where the deviation is larger. Events 1 and 2 specifically show two anticyclonic periods that are not captured by altimetry. These may explain some of the mismatch between simulations and observations. For example, the anticyclonic excursion in event 1 probably explains why the YBJ simulation results decay more quickly than observations. For event 2, the excursion occurs primarily near the start of the event, where the NIW amplitude is weak, so its effect is tempered. Many of these anomalies are short in duration, which limits the error in using the altimetric vorticity. The vorticity error for event 4a is minimal (Figure 9). We suspect the mismatch between the YBJ model and the observations in this event is due to the forcing. The reanalysis product used is not the exact wind-forcing felt at the OSMOSIS site. Both YBJ and PM show an initial peak in the NIW amplitude that is not seen in the observations, indicating that the wind-stress may be wrong at this point. The forcing event seen in observations then has to destroy these waves before forcing new ones, which causes the lower amplitude of the NIW peak in the YBJ simulation compared to observations. Notwithstanding the caveats above, it is significant that the YBJ model can reproduce much of the NIW evolution with only the mesoscale vorticity as derived from altimetry. One may expect the larger-magnitude submesoscale vorticity to be at least as important for the NIW evolution. But the dispersion term in the YBJ equation depends on the Laplacian of 𝑀 and hence in spectral space scales as 𝜅 2 . This means that the refractive generation of small-scale structure in the wave field will be opposed by increasingly strong dispersion. Our results therefore suggest that, at the location of the mooring array, dispersion indeed outpaces refraction at submesoscales and mesoscale refraction is more important for the NIW evolution (cf., Yu et al. 2022). Using a time-averaged stratification profile likely also contributes to differences between the observations and simulations, despite our attempts to keep simulation times as short as possible to avoid this effect. The assumption that the stratification does not vary in time is inherent in the YBJ scaling assumptions. Related to this is the question of what depth to force the model over. We used a fixed forcing depth, although this certainly varied over the simulation periods. This problem could be side-stepped by representing the wind forcing as a surface stress and adding a parameterized turbulent vertical momentum flux to the YBJ equation to transfer momentum from the wind downwards. The YBJ equation contains no term to represent the breaking of NIWs. The scaling 𝐻 ∗ = 𝑢 ∗ / √︁ 𝑁∗ 𝑓 , where 𝑢 ∗ = √︁ 𝜏/𝜌0 is the friction velocity and 𝑁 ∗ is the stratification at the base of the mixed layer, indicates the depth to which wind-driven turbulence could deepen the mixed layer (Pollard et al. 1973). If the mixed layer depth is shallower than 𝐻 ∗ , the effect of NIW dissipation would be important as there is potential for mixed layer deepening by breaking of NIWs (Plueddemann and Farrar 2006). During the OSMOSIS study, Yu et al. (2022) showed that the mixed layer was generally deeper than 𝐻 ∗ . This is especially true outside of summer and during the events we consider here. This is due to strong surface buoyancy forcing deepening the mixed layer by convection to a depth beyond what the winds alone could do. While one could include a critical Richardson number criterion to add NIW breaking to the YBJ equation, we believe that it is justifiable to ignore dissipation of NIWs in the surface layer in this study. In event 1, the wind work predicted by YBJ agreed well with that calculated by observations. The PM model greatly overestimated the wind-work. The YBJ and PM models also disagree on the wind work for all the other events (not shown). If mesoscale interactions change the alignment of the NIWs with the winds, then this results in a very different wind work. The difference in wind work between the YBJ and PM models depends on the degree to which the mesoscale changes the alignment of the waves with the wind and the power of the winds at different frequencies. The differences in wind work can be large for individual events but the five events we simulated are not enough to estimate what the average difference might be when averaged over many events. Nonetheless, this may provide motivation to revisit previous estimates of the NIW wind work in order to determine whether the mesoscale may modulate wind work into the NIW band globally. This paper is available on arxiv under CC 4.0 license. Authors: (1) Scott Conn, California Institute of Technology, Pasadena, California; (2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California; (3) Jorn Callies, California Institute of Technology, Pasadena, California. Authors: Authors: (1) Scott Conn, California Institute of Technology, Pasadena, California; (2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California; (3) Jorn Callies, California Institute of Technology, Pasadena, California. Table of Links Abstract and Intro Abstract and Intro Observations Observations Models Models Results Results Discussion Discussion Conclusion Conclusion APPENDIX A APPENDIX A APPENDIX B APPENDIX B APPENDIX C APPENDIX C References References 5. Discussion The YBJ model does well in reproducing the mooring observations of NIWs. There are still differences between the model and the observations, however, as well as a couple of events where the YBJ model does less well. Given the observational inputs to the model, it would be surprising if this were not the case. One major limitation is the use of altimetry for the mesoscale streamfunction. As mentioned previously, the altimetry data are a heavily smoothed version of the real field. We suggested above that some of the discrepancies between the YBJ model and the observations were due to this smoothing. We also interpolated the mesoscale vorticity onto a smaller simulation grid. The resolution of the altimetry product is 0.25◦×0.25◦ , which is larger than the size of the mooring array. Differences across the mooring array come from the interpolation between neighboring altimetry grid cells, which will have introduced interpolation errors. Furthermore, we assumed that the mesoscale eddy field was barotropic. This is a reasonable assumption if the vertical scale of the waves is much smaller than the vertical scale of the eddies. There are certainly errors in the YBJ evolution, however, that arise from neglecting the baroclinicity of mesoscale eddies. These effects could be investigated in the future by running similar simulations using an in-situ data set that resolves the vertical structure of one or more eddies. In event 1, the vorticity has large variations across the mooring array (Fig. 2a). This is reflected in the NIW observations as large differences in the amplitude across the mooring array. However, this need not be the case for all events. Event 3, by contrast, shows weak variations in the vorticity (as diagnosed from altimetry) across the mooring array. The result is that the YBJ simulations also show weak variations in the NIW field across the mooring array region. The altimetry vorticity field is a heavily smoothed representation of the real vorticity field of the ocean; smaller scale vorticity features are invisible to measurements from altimetry. If there is little variation in the larger-scale vorticity across the mooring array, then these smaller-scale vorticity features may play a more important role in governing the variations in 𝜕𝑧𝑀. While we do not have a spatial map of smaller-scale vorticity features, we can estimate their magnitude at the mooring array by calculating the vorticity by applying Stokes’ theorem to the area bounded by the outer moorings (Buckingham et al. 2016). The velocity that we use in Stokes’ theorem is low-pass filtered to estimate the balanced signal. This vorticity agrees in general with the vorticity calculated from SSH but shows more high-frequency variability (Fig. 9). Event 3 shows the biggest disagreement between the two estimates of all the events. The mooring estimate shows cyclonic vorticity, whereas the altimetry estimate shows anticyclonic vorticity. This likely explains why we see the amplitude decay much quicker in observations compared to simulations because there would have been a horizontal energy flux out of the region while the simulations have a flux into the region, which acts to maintain the amplitude. The other events show better agreement between the two vorticity estimates, although there are times where the deviation is larger. Events 1 and 2 specifically show two anticyclonic periods that are not captured by altimetry. These may explain some of the mismatch between simulations and observations. For example, the anticyclonic excursion in event 1 probably explains why the YBJ simulation results decay more quickly than observations. For event 2, the excursion occurs primarily near the start of the event, where the NIW amplitude is weak, so its effect is tempered. Many of these anomalies are short in duration, which limits the error in using the altimetric vorticity. The vorticity error for event 4a is minimal (Figure 9). We suspect the mismatch between the YBJ model and the observations in this event is due to the forcing. The reanalysis product used is not the exact wind-forcing felt at the OSMOSIS site. Both YBJ and PM show an initial peak in the NIW amplitude that is not seen in the observations, indicating that the wind-stress may be wrong at this point. The forcing event seen in observations then has to destroy these waves before forcing new ones, which causes the lower amplitude of the NIW peak in the YBJ simulation compared to observations. Notwithstanding the caveats above, it is significant that the YBJ model can reproduce much of the NIW evolution with only the mesoscale vorticity as derived from altimetry. One may expect the larger-magnitude submesoscale vorticity to be at least as important for the NIW evolution. But the dispersion term in the YBJ equation depends on the Laplacian of 𝑀 and hence in spectral space scales as 𝜅 2 . This means that the refractive generation of small-scale structure in the wave field will be opposed by increasingly strong dispersion. Our results therefore suggest that, at the location of the mooring array, dispersion indeed outpaces refraction at submesoscales and mesoscale refraction is more important for the NIW evolution (cf., Yu et al. 2022). Using a time-averaged stratification profile likely also contributes to differences between the observations and simulations, despite our attempts to keep simulation times as short as possible to avoid this effect. The assumption that the stratification does not vary in time is inherent in the YBJ scaling assumptions. Related to this is the question of what depth to force the model over. We used a fixed forcing depth, although this certainly varied over the simulation periods. This problem could be side-stepped by representing the wind forcing as a surface stress and adding a parameterized turbulent vertical momentum flux to the YBJ equation to transfer momentum from the wind downwards. The YBJ equation contains no term to represent the breaking of NIWs. The scaling 𝐻 ∗ = 𝑢 ∗ / √︁ 𝑁∗ 𝑓 , where 𝑢 ∗ = √︁ 𝜏/𝜌0 is the friction velocity and 𝑁 ∗ is the stratification at the base of the mixed layer, indicates the depth to which wind-driven turbulence could deepen the mixed layer (Pollard et al. 1973). If the mixed layer depth is shallower than 𝐻 ∗ , the effect of NIW dissipation would be important as there is potential for mixed layer deepening by breaking of NIWs (Plueddemann and Farrar 2006). During the OSMOSIS study, Yu et al. (2022) showed that the mixed layer was generally deeper than 𝐻 ∗ . This is especially true outside of summer and during the events we consider here. This is due to strong surface buoyancy forcing deepening the mixed layer by convection to a depth beyond what the winds alone could do. While one could include a critical Richardson number criterion to add NIW breaking to the YBJ equation, we believe that it is justifiable to ignore dissipation of NIWs in the surface layer in this study. In event 1, the wind work predicted by YBJ agreed well with that calculated by observations. The PM model greatly overestimated the wind-work. The YBJ and PM models also disagree on the wind work for all the other events (not shown). If mesoscale interactions change the alignment of the NIWs with the winds, then this results in a very different wind work. The difference in wind work between the YBJ and PM models depends on the degree to which the mesoscale changes the alignment of the waves with the wind and the power of the winds at different frequencies. The differences in wind work can be large for individual events but the five events we simulated are not enough to estimate what the average difference might be when averaged over many events. Nonetheless, this may provide motivation to revisit previous estimates of the NIW wind work in order to determine whether the mesoscale may modulate wind work into the NIW band globally. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

A Deep Discussion On Our Study Looking at Near-Inertial Waves and Mesoscale Eddies: Diving In

The Results We Got After Observing Interactions Between Near-Inertial Waves and Mesoscale Eddies

Authors:
(1) Scott Conn, California Institute of Technology, Pasadena, California;
(2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California;
(3) Jorn Callies, California Institute of Technology, Pasadena, California. Table of Links Abstract and Intro Observations Models Results Discussion Conclusion APPENDIX A APPENDIX B APPENDIX C References 3. Models a. The PM Model For each event, we use a constant mixed layer depth that is an average of the time-varying mixed layer depth over duration of the event. Since the events are relatively short, the error in this approximation is minimal for most events. We make this choice of a constant mixed layer depth to avoid complications that arise otherwise, especially in the YBJ model discussed below. b. The YBJ Model The YBJ equation is a three-dimensional partial differential equation, making it substantially more computationally expensive to integrate than the PM model. We solve the YBJ equation using the pseudospectral solver Dedalus (Burns et al. 2020) with a mixed explicit and implicit diagonal RK2 scheme. As discussed above, we start the simulations with no waves. We use a domain that is 400 km×400 km in the horizontal (centered on the mooring array) and 4 km deep. Each dimension is discretized with 128 modes. The vertical dimension is finite and represented using Chebyshev polynomials. The horizontal dimensions are made periodic and represented using Fourier modes. The stratification and the wind forcing are taken to be horizontally uniform, capturing the forcing at a scale much larger than the mesoscale. Smaller-scale structure in the wind stress can generate smaller-scale NIWs, but the energy input tends to be strongly dominated by the large-scale winds (Rama et al. 2022). To construct the mesoscale streamfunction used in the simulations, we take 𝜓 from observations and calculate the vorticity by taking the finite-difference Laplacian of 𝜓 on the sphere. We then interpolate this vorticity onto the Cartesian simulation grid centered on the location of the central mooring. We apply a taper to the vorticity, such that it goes to zero on the domain boundaries. We invert this tapered vorticity field for the streamfunction on the periodic domain, making the resulting streamfunction periodic as well. Our conclusions are neither sensitive to the form nor width of the taper. For the results shown below, we use the following form of the taper: When the winds blow on the ocean surface, they generate turbulence that mixes momentum downwards. If a mixed layer already exists and is not too deep, the momentum input from the wind will be rapidly homogenized within the mixed layer (Pollard and Millard 1970; Kato and Phillips 1969). For some events at the OSMOSIS site, the mixed layer was up to a few hundred meters deep. These deep mixed layers are likely the result of convection driven by buoyancy forcing rather than the mechanical wind forcing (Thompson et al. 2016). In these cases, it is unlikely that the momentum is uniform across the mixed layer, especially if the buoyancy forcing has ceased. The depth structure of NIWs obtained from the OSMOSIS mooring confirms this picture. The waves are initially forced over a layer that is thinner than the mixed layer before they propagate to depth. To avoid forcing over an unrealistically large depth, we cap the forcing layer at 80 m. This value is guided by the observations and represents an average depth over which waves are forced when the mixed layer is deep. We discuss possible ways to improve this representation below. In order to solve the YBJ equation, we must further specify vertical boundary conditions. The requirement that the vertical velocity is zero on the top and bottom of the domain translates to the requirement that 𝑀 be horizontally uniform at the top and bottom boundaries (Young and Ben Jelloul 1997). Since 𝑀 is determined by 𝜕𝑧𝑀 up to an arbitrary horizontal function, without loss of generality we specify 𝑀(𝑥, 𝑦,−𝐻,𝑡) = 0. The top boundary condition can be found by vertically integrating the YBJ equation twice and requiring that 𝑀 be horizontally uniform at 𝑧 = 0 (Appendix B). The result is which we integrate a priori and then use as a Dirichlet boundary condition on 𝑀. This paper is available on arxiv under CC 4.0 license. Authors: (1) Scott Conn, California Institute of Technology, Pasadena, California; (2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California; (3) Jorn Callies, California Institute of Technology, Pasadena, California. Authors: Authors: (1) Scott Conn, California Institute of Technology, Pasadena, California; (2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California; (3) Jorn Callies, California Institute of Technology, Pasadena, California. Table of Links Abstract and Intro Abstract and Intro Observations Observations Models Models Results Results Discussion Discussion Conclusion Conclusion APPENDIX A APPENDIX A APPENDIX B APPENDIX B APPENDIX C APPENDIX C References References 3. Models a. The PM Model a. The PM Model For each event, we use a constant mixed layer depth that is an average of the time-varying mixed layer depth over duration of the event. Since the events are relatively short, the error in this approximation is minimal for most events. We make this choice of a constant mixed layer depth to avoid complications that arise otherwise, especially in the YBJ model discussed below. b. The YBJ Model b. The YBJ Model The YBJ equation is a three-dimensional partial differential equation, making it substantially more computationally expensive to integrate than the PM model. We solve the YBJ equation using the pseudospectral solver Dedalus (Burns et al. 2020) with a mixed explicit and implicit diagonal RK2 scheme. As discussed above, we start the simulations with no waves. We use a domain that is 400 km×400 km in the horizontal (centered on the mooring array) and 4 km deep. Each dimension is discretized with 128 modes. The vertical dimension is finite and represented using Chebyshev polynomials. The horizontal dimensions are made periodic and represented using Fourier modes. The stratification and the wind forcing are taken to be horizontally uniform, capturing the forcing at a scale much larger than the mesoscale. Smaller-scale structure in the wind stress can generate smaller-scale NIWs, but the energy input tends to be strongly dominated by the large-scale winds (Rama et al. 2022). To construct the mesoscale streamfunction used in the simulations, we take 𝜓 from observations and calculate the vorticity by taking the finite-difference Laplacian of 𝜓 on the sphere. We then interpolate this vorticity onto the Cartesian simulation grid centered on the location of the central mooring. We apply a taper to the vorticity, such that it goes to zero on the domain boundaries. We invert this tapered vorticity field for the streamfunction on the periodic domain, making the resulting streamfunction periodic as well. Our conclusions are neither sensitive to the form nor width of the taper. For the results shown below, we use the following form of the taper: When the winds blow on the ocean surface, they generate turbulence that mixes momentum downwards. If a mixed layer already exists and is not too deep, the momentum input from the wind will be rapidly homogenized within the mixed layer (Pollard and Millard 1970; Kato and Phillips 1969). For some events at the OSMOSIS site, the mixed layer was up to a few hundred meters deep. These deep mixed layers are likely the result of convection driven by buoyancy forcing rather than the mechanical wind forcing (Thompson et al. 2016). In these cases, it is unlikely that the momentum is uniform across the mixed layer, especially if the buoyancy forcing has ceased. The depth structure of NIWs obtained from the OSMOSIS mooring confirms this picture. The waves are initially forced over a layer that is thinner than the mixed layer before they propagate to depth. To avoid forcing over an unrealistically large depth, we cap the forcing layer at 80 m. This value is guided by the observations and represents an average depth over which waves are forced when the mixed layer is deep. We discuss possible ways to improve this representation below. In order to solve the YBJ equation, we must further specify vertical boundary conditions. The requirement that the vertical velocity is zero on the top and bottom of the domain translates to the requirement that 𝑀 be horizontally uniform at the top and bottom boundaries (Young and Ben Jelloul 1997). Since 𝑀 is determined by 𝜕𝑧𝑀 up to an arbitrary horizontal function, without loss of generality we specify 𝑀(𝑥, 𝑦,−𝐻,𝑡) = 0. The top boundary condition can be found by vertically integrating the YBJ equation twice and requiring that 𝑀 be horizontally uniform at 𝑧 = 0 (Appendix B). The result is which we integrate a priori and then use as a Dirichlet boundary condition on 𝑀. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

The Models We Used to Observed Interactions Between Near-Inertial Waves and Mesoscale Eddies

Authors:
(1) Scott Conn, California Institute of Technology, Pasadena, California;
(2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California;
(3) Jorn Callies, California Institute of Technology, Pasadena, California. Table of Links Abstract and Intro Observations Models Results Discussion Conclusion APPENDIX A APPENDIX B APPENDIX C References 2. Observations a. NIW Data We extract observations of NIWs from data collected for the Ocean Surface Mixing, Ocean Submesoscale Interaction Study (OSMOSIS; Buckingham et al. 2016). As part of the study, measurements were taken from nine moorings anchored over the Porcupine Abyssal Plain in the northeastern part of the Atlantic Ocean from September 2012 to September 2013. The moorings were all distributed less than 10 km from a central mooring located at (48.6875◦N, −16.1875◦E) (Fig. 1a,b). In this study, we focus on observations from the central mooring and the four outermost moorings. Each mooring took measurements of the horizontal velocity once every ten minutes using an acoustic current meter (ACM). On the central mooring, there were 13 ACMs spaced nominally between 50 m and 500 m depth. On the outer moorings there were five ACMs nominally spaced over the same depth range. The deepest ACM failed on the outer northeast (ONE) mooring, and so measurements are only available to a depth of 361 m. The actual depth of the instruments varied in time due to drag exerted by the flow on the moorings. Over the course of the year, there were several times where the moorings experienced knockdown by up to 200 m (Callies et al. 2020). We flag these events if the knockdown on the central mooring is more than 10 m when averaged with a 1-day running mean. Outside of these knockdown events the variations in mooring depth about the nominal depth is ∼2 m. The interpretation of the observed NIW signal during these knockdown events is complicated because the filter we use to extract the NIW signal does not commute with evaluating the signal along the trajectory of the ACMs. We do not attempt to explain the observations during the knockdown periods. b. Stratification and mixed layer Depth c. Wind Data d. Altimetry To characterize the mesoscale eddy field, we use observations of the sea surface height (SSH) from the Data Unification and Altimeter Combination System’s (DUACS) delayed-time (DT) 2018 release (Taburet et al. 2019). The DUACS DT2018 SSH maps are provided at a nominal (1/4) ◦ and daily resolution. We convert these measurements to a geostrophic streamfunction using 𝜓 = 𝑔ℎ/ 𝑓 , where ℎ is the SSH and 𝑓 is the latitude-dependent Coriolis parameter. This paper is available on arxiv under CC 4.0 license. Authors: (1) Scott Conn, California Institute of Technology, Pasadena, California; (2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California; (3) Jorn Callies, California Institute of Technology, Pasadena, California. Authors: Authors: (1) Scott Conn, California Institute of Technology, Pasadena, California; (2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California; (3) Jorn Callies, California Institute of Technology, Pasadena, California. Table of Links Abstract and Intro Abstract and Intro Observations Observations Models Models Results Results Discussion Discussion Conclusion Conclusion APPENDIX A APPENDIX A APPENDIX B APPENDIX B APPENDIX C APPENDIX C References References 2. Observations a. NIW Data a. NIW Data We extract observations of NIWs from data collected for the Ocean Surface Mixing, Ocean Submesoscale Interaction Study (OSMOSIS; Buckingham et al. 2016). As part of the study, measurements were taken from nine moorings anchored over the Porcupine Abyssal Plain in the northeastern part of the Atlantic Ocean from September 2012 to September 2013. The moorings were all distributed less than 10 km from a central mooring located at (48.6875◦N, −16.1875◦E) (Fig. 1a,b). In this study, we focus on observations from the central mooring and the four outermost moorings. Each mooring took measurements of the horizontal velocity once every ten minutes using an acoustic current meter (ACM). On the central mooring, there were 13 ACMs spaced nominally between 50 m and 500 m depth. On the outer moorings there were five ACMs nominally spaced over the same depth range. The deepest ACM failed on the outer northeast (ONE) mooring, and so measurements are only available to a depth of 361 m. The actual depth of the instruments varied in time due to drag exerted by the flow on the moorings. Over the course of the year, there were several times where the moorings experienced knockdown by up to 200 m (Callies et al. 2020). We flag these events if the knockdown on the central mooring is more than 10 m when averaged with a 1-day running mean. Outside of these knockdown events the variations in mooring depth about the nominal depth is ∼2 m. The interpretation of the observed NIW signal during these knockdown events is complicated because the filter we use to extract the NIW signal does not commute with evaluating the signal along the trajectory of the ACMs. We do not attempt to explain the observations during the knockdown periods. b. Stratification and mixed layer Depth b. Stratification and mixed layer Depth c. Wind Data c. Wind Data d. Altimetry d. Altimetry To characterize the mesoscale eddy field, we use observations of the sea surface height (SSH) from the Data Unification and Altimeter Combination System’s (DUACS) delayed-time (DT) 2018 release (Taburet et al. 2019). The DUACS DT2018 SSH maps are provided at a nominal (1/4) ◦ and daily resolution. We convert these measurements to a geostrophic streamfunction using 𝜓 = 𝑔ℎ/ 𝑓 , where ℎ is the SSH and 𝑓 is the latitude-dependent Coriolis parameter. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

How We Observed Interactions Between Near-Inertial Waves and Mesoscale Eddies and What We Found

Authors:
(1) Scott Conn, California Institute of Technology, Pasadena, California;
(2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California;
(3) Jorn Callies, California Institute of Technology, Pasadena, California. Table of Links Abstract and Intro Observations Models Results Discussion Conclusion APPENDIX A APPENDIX B APPENDIX C References ABSTRACT The evolution of wind-generated near-inertial waves (NIWs) is known to be influenced by the mesoscale eddy field, yet it remains a challenge to disentangle the effects of this interaction in observations. Here, the model of Young and Ben Jelloul (YBJ), which describes NIW evolution in the presence of slowly evolving mesoscale eddies, is compared to observations from a mooring array in the Northeast Atlantic Ocean. The model captures the evolution of both the observed NIW amplitude and phase much more accurately than a slab mixed layer model. The YBJ model allows for the identification of specific physical processes that drive the observed evolution. It reveals that differences in the NIW amplitude across the mooring array are caused by the refractive concentration of NIWs into anticyclones. Advection and wave dispersion also make important contributions to the observed wave evolution. Stimulated generation, a process by which mesoscale kinetic energy acts as a source of NIW potential energy, is estimated to be 20 µW m−2 in the region of the mooring array, which is two orders of magnitude smaller than the global average input to mesoscale kinetic energy and likely not an important contribution to the mesoscale kinetic energy budget in this region. Overall, the results show that the YBJ model is a quantitatively useful tool to interpret observations of NIWs. 1. Introduction Near-inertial waves (NIWs), internal waves with a frequency close to the inertial frequency 𝑓 , are resonantly excited by atmospheric winds exerting a stress on the ocean’s surface. It has long been recognized that these waves can interact with mesoscale eddies and that this interaction may be important in the life cycle of wind-generated NIWs. Observational evidence of NIW–mesoscale interactions is accumulating, but interpreting the observed NIW evolution in the presence of mesoscale eddies remains challenging. Here, we employ the theoretical framework of Young and Ben Jelloul (1997, from hereon YBJ) to identify and interpret such interactions in mooring observations in the Northeast Atlantic Ocean. NIWs are associated with a large vertical shear, which can result in shear instabilities and vertical mixing (for a review, see Alford et al. 2016). These shear instabilities are a key mechanism by which atmospheric storms can cause the surface mixed layer to deepen. Jochum et al. (2013) showed that an improved representation of NIWs in a climate model led to a deepening of the mixed layer on average, which in turn resulted in significant changes in sea surface temperatures, winds, and precipitation. It has also been proposed that NIWs not only react to the presence of mesoscale eddies but feed back on the eddies and affect their evolution. Approximately 80% of the ocean’s kinetic energy exists as mesoscale motions (Ferrari and Wunsch 2009). The geostrophic constraint on mesoscale eddies traps energy at large scales, and it is not entirely clear how the energy input into mesoscale motion is balanced by dissipation (M¨uller et al. 2011). A number of mechanisms by which mesoscale eddies lose energy are known, including dissipation in bottom boundary layers (e.g., Arbic and Flierl 2004), the generation of dissipative lee waves (e.g., Nikurashin et al. 2013), energy loss near western boundaries (e.g., Zhai et al. 2010), and the top drag arising from the current dependence of the wind stress (e.g., Dewar and Flierl 1987; Renault et al. 2016). The extraction of energy from mesoscale eddies by NIWs presents another possibility (Xie and Vanneste 2015; Rocha et al. 2018). Given the great importance of mesoscale eddies to the transport of heat and carbon (e.g., Jayne and Marotzke 2002; Gnanadesikan et al. 2015), even small changes (see discussion in Asselin and Young 2020) to the mesoscale eddy field caused by NIWs may be significant to the impact of the ocean on climate. Despite its successes in capturing some aspects of the observed NIW signal, the PM model cannot explain the propagation of NIWs out of the mixed layer. If the NIW field is initially uniform, it will remain so. The model captures neither 𝛽-refraction nor the interaction with mesoscale eddies. This interpretation of the Ocean Storms Experiment was pursued further by Balmforth et al. (1998), who ran spin-down simulations of the YBJ equation. NIWs were initialized in the mixed layer and evolved in the presence of an idealized, barotropic mesoscale eddy field. Qualitative comparisons between the simulations and observations showed that YBJ dynamics were not inconsistent with the observed time for NIWs to escape the mixed layer. Balmforth and Young (1999) showed that including the 𝛽-effect improved the agreement with observations. Because an idealized eddy field was used, however, no quantitative conclusions could be drawn about the ability of YBJ to capture the observed evolution. In this study, we aim to bridge the gap between theory and observations by using the YBJ framework to interpret the observed evolution of NIWs in the Northeast Atlantic Ocean. We use an array of nine moorings to capture some of the mesoscale variations in the NIW field. The YBJ framework allows us to attribute the observed NIW evolution to a set of well-defined physical processes. We integrate the three-dimensional YBJ equation using observational inputs for the wind forcing, mesoscale streamfunction, and stratification, and we compare these simulations to simpler slab models. We show that the YBJ model offers significant improvements in modeling NIW evolution, without the need for any tuning. We use the YBJ energy budgets to provide a dynamical interpretation of spatial and temporal variations in the NIW field and quantify the relative importance of the various physical processes involved. We also provide an estimate for the importance of stimulated generation in this region. This paper is available on arxiv under CC 4.0 license. Authors: (1) Scott Conn, California Institute of Technology, Pasadena, California; (2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California; (3) Jorn Callies, California Institute of Technology, Pasadena, California. Authors: Authors: (1) Scott Conn, California Institute of Technology, Pasadena, California; (2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California; (3) Jorn Callies, California Institute of Technology, Pasadena, California. Table of Links Abstract and Intro Abstract and Intro Observations Observations Models Models Results Results Discussion Discussion Conclusion Conclusion APPENDIX A APPENDIX A APPENDIX B APPENDIX B APPENDIX C APPENDIX C References References ABSTRACT The evolution of wind-generated near-inertial waves (NIWs) is known to be influenced by the mesoscale eddy field, yet it remains a challenge to disentangle the effects of this interaction in observations. Here, the model of Young and Ben Jelloul (YBJ), which describes NIW evolution in the presence of slowly evolving mesoscale eddies, is compared to observations from a mooring array in the Northeast Atlantic Ocean. The model captures the evolution of both the observed NIW amplitude and phase much more accurately than a slab mixed layer model. The YBJ model allows for the identification of specific physical processes that drive the observed evolution. It reveals that differences in the NIW amplitude across the mooring array are caused by the refractive concentration of NIWs into anticyclones. Advection and wave dispersion also make important contributions to the observed wave evolution. Stimulated generation, a process by which mesoscale kinetic energy acts as a source of NIW potential energy, is estimated to be 20 µW m−2 in the region of the mooring array, which is two orders of magnitude smaller than the global average input to mesoscale kinetic energy and likely not an important contribution to the mesoscale kinetic energy budget in this region. Overall, the results show that the YBJ model is a quantitatively useful tool to interpret observations of NIWs. 1. Introduction Near-inertial waves (NIWs), internal waves with a frequency close to the inertial frequency 𝑓 , are resonantly excited by atmospheric winds exerting a stress on the ocean’s surface. It has long been recognized that these waves can interact with mesoscale eddies and that this interaction may be important in the life cycle of wind-generated NIWs. Observational evidence of NIW–mesoscale interactions is accumulating, but interpreting the observed NIW evolution in the presence of mesoscale eddies remains challenging. Here, we employ the theoretical framework of Young and Ben Jelloul (1997, from hereon YBJ) to identify and interpret such interactions in mooring observations in the Northeast Atlantic Ocean. NIWs are associated with a large vertical shear, which can result in shear instabilities and vertical mixing (for a review, see Alford et al. 2016). These shear instabilities are a key mechanism by which atmospheric storms can cause the surface mixed layer to deepen. Jochum et al. (2013) showed that an improved representation of NIWs in a climate model led to a deepening of the mixed layer on average, which in turn resulted in significant changes in sea surface temperatures, winds, and precipitation. It has also been proposed that NIWs not only react to the presence of mesoscale eddies but feed back on the eddies and affect their evolution. Approximately 80% of the ocean’s kinetic energy exists as mesoscale motions (Ferrari and Wunsch 2009). The geostrophic constraint on mesoscale eddies traps energy at large scales, and it is not entirely clear how the energy input into mesoscale motion is balanced by dissipation (M¨uller et al. 2011). A number of mechanisms by which mesoscale eddies lose energy are known, including dissipation in bottom boundary layers (e.g., Arbic and Flierl 2004), the generation of dissipative lee waves (e.g., Nikurashin et al. 2013), energy loss near western boundaries (e.g., Zhai et al. 2010), and the top drag arising from the current dependence of the wind stress (e.g., Dewar and Flierl 1987; Renault et al. 2016). The extraction of energy from mesoscale eddies by NIWs presents another possibility (Xie and Vanneste 2015; Rocha et al. 2018). Given the great importance of mesoscale eddies to the transport of heat and carbon (e.g., Jayne and Marotzke 2002; Gnanadesikan et al. 2015), even small changes (see discussion in Asselin and Young 2020) to the mesoscale eddy field caused by NIWs may be significant to the impact of the ocean on climate. Despite its successes in capturing some aspects of the observed NIW signal, the PM model cannot explain the propagation of NIWs out of the mixed layer. If the NIW field is initially uniform, it will remain so. The model captures neither 𝛽-refraction nor the interaction with mesoscale eddies. This interpretation of the Ocean Storms Experiment was pursued further by Balmforth et al. (1998), who ran spin-down simulations of the YBJ equation. NIWs were initialized in the mixed layer and evolved in the presence of an idealized, barotropic mesoscale eddy field. Qualitative comparisons between the simulations and observations showed that YBJ dynamics were not inconsistent with the observed time for NIWs to escape the mixed layer. Balmforth and Young (1999) showed that including the 𝛽-effect improved the agreement with observations. Because an idealized eddy field was used, however, no quantitative conclusions could be drawn about the ability of YBJ to capture the observed evolution. In this study, we aim to bridge the gap between theory and observations by using the YBJ framework to interpret the observed evolution of NIWs in the Northeast Atlantic Ocean. We use an array of nine moorings to capture some of the mesoscale variations in the NIW field. The YBJ framework allows us to attribute the observed NIW evolution to a set of well-defined physical processes. We integrate the three-dimensional YBJ equation using observational inputs for the wind forcing, mesoscale streamfunction, and stratification, and we compare these simulations to simpler slab models. We show that the YBJ model offers significant improvements in modeling NIW evolution, without the need for any tuning. We use the YBJ energy budgets to provide a dynamical interpretation of spatial and temporal variations in the NIW field and quantify the relative importance of the various physical processes involved. We also provide an estimate for the importance of stimulated generation in this region. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Interpreting Observed Interactions Between Near-Inertial Waves and Mesoscale Eddies

Authors:
(1) Hans van Haren, NIOZ Royal Netherlands Institute for Sea Research, P.O. Box 59, 1790 AB Den Burg, the Netherlands. Table of Links Abstract and Intro Data Observations Simulating Transition Discussion Conclusions and References 6 Conclusions Acknowledgments I thank the crews of the R/V Thethys II and Le Suroît for the sea operations, G. Rougier and C. Millot for preparing the ‘GYROSCOP-2’ mooring, and T. Gerkema for providing the model results. I gratefully acknowledge support from the Netherlands organisation for the advancement of scientific research, NWO, and Centre National de la Recherche Scientifique, CNRS, under the (alas no longer existing) French Dutch scientific collaboration. References Abarbanel HDI, Holm DD, Marsden JE, Ratiu T (1984) Richardson number criterion for the nonlinear stability of three-dimensional stratified flow. Phys Rev Lett 52:2352-2355 Dengler M, Quadfasel D (2002) Equatorial deep jets and abyssal mixing in the Indian Ocean. J Phys Oceanogr 32:1165-1180 Gascard J-C (1973) Vertical motions in a region of deep water formation. Deep-Sea Res 20:1011-1027 Gerkema T, Shrira VI (2005) Near-inertial waves on the “nontraditional”  plane. J Geophys Res 110:C01003. doi:10.1029/2004JC002519 Gerkema T, Exarchou E (2008) Internal-wave properties in weakly stratified layers. J Mar Res 66:617-644 Gerkema T, Zimmerman JTF, Maas LRM, van Haren H (2008) Geophysical and astrophysical fluid dynamics beyond the traditional approximation. Rev Geophys 46:RG2004. doi:10.1029/2006RG000220 Gill AE (1982) Atmosphere-Ocean Dynamics. Academic Press, San Diego, pp 1-680 Gonella J (1972) A rotary-component method for analysing meteorological and oceanographic vector time series. Deep-Sea Res 19:833-846 Howard LN (1961) Note on a paper of John W. Miles. J. Fluid Mech 10:509-512 LeBlond PH, Mysak LA (1978) Waves in the ocean. Elsevier, Amsterdam, pp 1-602 Marshall J, Schott F (1999) Open-ocean convection: observations, theory, and models. Rev Geophys 37:1-64 Matsuno T, Endoh T, Hibiya T, Sengyu T, Watanabe M (2015) Formation of the well‑mixed homogeneous layer in the bottom water of the Japan Sea. J Oceanogr 71:441-447 Miles JW (1961) On the stability of heterogeneous shear flows. J Fluid Mech 10:496-508 Millot C (1999) Circulation in the Western Mediterranean Sea. J Mar Sys 20:423-442 Millot C, Monaco A (1984) Deep strong currents and sediment transport in the Northwestern Mediterranean Sea. Geo-Mar Lett 4:13-17 Morozov EG, Velarde MG (2008) Inertial oscillations as deep ocean response to hurricanes. J Oceanogr 64:495-509 Munk WH (1980) Internal wave spectra at the buoyant and inertial frequencies. J Phys Oceanogr 10:1718-1728 Saint-Guily B (1970) On internal waves, effects of the horizontal component of the Earth’s rotation and of a uniform current. D Hyd Z 23:16-23 Schott F, Leaman K (1991) Observations with moored acoustic Doppler current profilers in the convection regime in the Golfe du Lion. J Phys Oceanogr 21:558-574 Shay LK, Elsberry RL (1987) Near-inertial ocean current response to hurricane Frederic. J Phys Oceanogr 17:1249-1269 Sheremet VA (2004) Laboratory experiments with tilted convective plumes on a centrifuge: a finite angle between the buoyancy and the axis of rotation. J Fluid Mech 506:217-244 Straneo F, Kawase M, Riser SC (2002) Idealized models of slantwise convection in a baroclinic flow. J Phys Oceanogr 32:558-572 Talley LD, Lohmov V, Ponomarev V, Salyuk A, Tishchenko P, Zhabin I, Riser S (2009) Deep convection and brine rejection in the Japan Sea. Geophys Res Lett 30:1159. doi: 10.1029/2002GL016451 Timmermans M-L, Melling H, Rainville L (2007) Dynamics in the deep Canada Basin, Arctic Ocean, inferred by thermistor chain time series. J Phys Oceanogr 37:1066-1076 van Haren H (2006) Asymmetric vertical internal wave propagation. Geophys Res Lett 33:L06618. doi:10.1029/2005GL025499 van Haren H (2008) Abrupt transitions between gyroscopic and internal gravity waves: the mid-latitude case. J Fluid Mech 598:67-80 van Haren H, Millot C (2004) Rectilinear and circular inertial motions in the Western Mediterranean Sea. Deep-Sea Res I 51:1441-1455 van Haren H, Millot C (2005) Gyroscopic waves in the Mediterranean Sea. Geophys Res Lett 32:L24614. doi:10.1029/2005GL023915 van Haren H, Millot C (2009) Slantwise convection: a candidate for homogenization of deep newly formed dense waters. Geophys Res Lett 36:L12604. doi:10.1029/2009GL038736 van Haren H, Millot C, Taupier-Letage I (2006) Fast deep sinking in Mediterranean eddies. Geophys Res Lett 33:L04606. doi:10.1029/2005GL025367 Voorhis AD, Webb DC (1970). Large vertical currents observed in a winter sinking region of the northwestern Mediterranean. Cah océanogr 22:571-580 This paper is available on arxiv under CC 4.0 license. Authors: (1) Hans van Haren, NIOZ Royal Netherlands Institute for Sea Research, P.O. Box 59, 1790 AB Den Burg, the Netherlands. Authors: Authors: (1) Hans van Haren, NIOZ Royal Netherlands Institute for Sea Research, P.O. Box 59, 1790 AB Den Burg, the Netherlands. Table of Links Abstract and Intro Abstract and Intro Data Data Observations Observations Simulating Transition Simulating Transition Discussion Discussion Conclusions and References Conclusions and References 6 Conclusions Acknowledgments I thank the crews of the R/V Thethys II and Le Suroît for the sea operations, G. Rougier and C. Millot for preparing the ‘GYROSCOP-2’ mooring, and T. Gerkema for providing the model results. I gratefully acknowledge support from the Netherlands organisation for the advancement of scientific research, NWO, and Centre National de la Recherche Scientifique, CNRS, under the (alas no longer existing) French Dutch scientific collaboration. Acknowledgments References Abarbanel HDI, Holm DD, Marsden JE, Ratiu T (1984) Richardson number criterion for the nonlinear stability of three-dimensional stratified flow. Phys Rev Lett 52:2352-2355 Dengler M, Quadfasel D (2002) Equatorial deep jets and abyssal mixing in the Indian Ocean. J Phys Oceanogr 32:1165-1180 Gascard J-C (1973) Vertical motions in a region of deep water formation. Deep-Sea Res 20:1011-1027 Gerkema T, Shrira VI (2005) Near-inertial waves on the “nontraditional”  plane. J Geophys Res 110:C01003. doi:10.1029/2004JC002519 Gerkema T, Exarchou E (2008) Internal-wave properties in weakly stratified layers. J Mar Res 66:617-644 Gerkema T, Zimmerman JTF, Maas LRM, van Haren H (2008) Geophysical and astrophysical fluid dynamics beyond the traditional approximation. Rev Geophys 46:RG2004. doi:10.1029/2006RG000220 Gill AE (1982) Atmosphere-Ocean Dynamics. Academic Press, San Diego, pp 1-680 Gonella J (1972) A rotary-component method for analysing meteorological and oceanographic vector time series. Deep-Sea Res 19:833-846 Howard LN (1961) Note on a paper of John W. Miles. J. Fluid Mech 10:509-512 LeBlond PH, Mysak LA (1978) Waves in the ocean. Elsevier, Amsterdam, pp 1-602 Marshall J, Schott F (1999) Open-ocean convection: observations, theory, and models. Rev Geophys 37:1-64 Matsuno T, Endoh T, Hibiya T, Sengyu T, Watanabe M (2015) Formation of the well‑mixed homogeneous layer in the bottom water of the Japan Sea. J Oceanogr 71:441-447 Miles JW (1961) On the stability of heterogeneous shear flows. J Fluid Mech 10:496-508 Millot C (1999) Circulation in the Western Mediterranean Sea. J Mar Sys 20:423-442 Millot C, Monaco A (1984) Deep strong currents and sediment transport in the Northwestern Mediterranean Sea. Geo-Mar Lett 4:13-17 Morozov EG, Velarde MG (2008) Inertial oscillations as deep ocean response to hurricanes. J Oceanogr 64:495-509 Munk WH (1980) Internal wave spectra at the buoyant and inertial frequencies. J Phys Oceanogr 10:1718-1728 Saint-Guily B (1970) On internal waves, effects of the horizontal component of the Earth’s rotation and of a uniform current. D Hyd Z 23:16-23 Schott F, Leaman K (1991) Observations with moored acoustic Doppler current profilers in the convection regime in the Golfe du Lion. J Phys Oceanogr 21:558-574 Shay LK, Elsberry RL (1987) Near-inertial ocean current response to hurricane Frederic. J Phys Oceanogr 17:1249-1269 Sheremet VA (2004) Laboratory experiments with tilted convective plumes on a centrifuge: a finite angle between the buoyancy and the axis of rotation. J Fluid Mech 506:217-244 Straneo F, Kawase M, Riser SC (2002) Idealized models of slantwise convection in a baroclinic flow. J Phys Oceanogr 32:558-572 Talley LD, Lohmov V, Ponomarev V, Salyuk A, Tishchenko P, Zhabin I, Riser S (2009) Deep convection and brine rejection in the Japan Sea. Geophys Res Lett 30:1159. doi: 10.1029/2002GL016451 Timmermans M-L, Melling H, Rainville L (2007) Dynamics in the deep Canada Basin, Arctic Ocean, inferred by thermistor chain time series. J Phys Oceanogr 37:1066-1076 van Haren H (2006) Asymmetric vertical internal wave propagation. Geophys Res Lett 33:L06618. doi:10.1029/2005GL025499 van Haren H (2008) Abrupt transitions between gyroscopic and internal gravity waves: the mid-latitude case. J Fluid Mech 598:67-80 van Haren H, Millot C (2004) Rectilinear and circular inertial motions in the Western Mediterranean Sea. Deep-Sea Res I 51:1441-1455 van Haren H, Millot C (2005) Gyroscopic waves in the Mediterranean Sea. Geophys Res Lett 32:L24614. doi:10.1029/2005GL023915 van Haren H, Millot C (2009) Slantwise convection: a candidate for homogenization of deep newly formed dense waters. Geophys Res Lett 36:L12604. doi:10.1029/2009GL038736 van Haren H, Millot C, Taupier-Letage I (2006) Fast deep sinking in Mediterranean eddies. Geophys Res Lett 33:L04606. doi:10.1029/2005GL025367 Voorhis AD, Webb DC (1970). Large vertical currents observed in a winter sinking region of the northwestern Mediterranean. Cah océanogr 22:571-580 This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Near-inertial wave propagation between stratified and homogeneous layers: Conclusions and References

Authors:
(1) Hans van Haren, NIOZ Royal Netherlands Institute for Sea Research, P.O. Box 59, 1790 AB Den Burg, the Netherlands. Table of Links Abstract and Intro Data Observations Simulating Transition Discussion Conclusions and References 5 Discussion As a result, inertial motions, the dominant propagating motions, may initiate similar convective mixing in stratified layers, which is equivalent to slantwise homogeneous, and vertically homogeneous layers, resulting in continuous T-S property variations across the stratification interface (e.g., van Haren and Millot (2009). By the same token, the difference in f-motions in the different layers will be differently polarized, and hence shear will change. To complicate things further, indications like variations in horizontal current polarization, changing from near-circular to increasingly elliptic, may vary strongly in the vertical, as has been shown in a numerical model (Gerkema and Exarchou, 2008). This may ‘explain’ the observed z,t-variable polarization for near-inertial horizontal motions (Fig. 9). Generally, near-f motions generate most shear because of their short vertical scales in stratified waters, especially in the Mediterranean where tides are also weak, resulting in generation of diapycnal turbulent overturning and mixing. Needless to say that the complex inertial internal wave propagation which is capable of un-attenuated border-crossing between homogeneous and stratified layers, will influence turbulent mixing in the deep. However, more future observational and modelling studies, also from other weakly stratified basins, are wanted for the precise mechanisms of deep-sea mixing that is so relevant for life in the abyss. This paper is available on arxiv under CC 4.0 license. Authors: (1) Hans van Haren, NIOZ Royal Netherlands Institute for Sea Research, P.O. Box 59, 1790 AB Den Burg, the Netherlands. Authors: Authors: (1) Hans van Haren, NIOZ Royal Netherlands Institute for Sea Research, P.O. Box 59, 1790 AB Den Burg, the Netherlands. Table of Links Abstract and Intro Abstract and Intro Data Data Observations Observations Simulating Transition Simulating Transition Discussion Discussion Conclusions and References Conclusions and References 5 Discussion As a result, inertial motions, the dominant propagating motions, may initiate similar convective mixing in stratified layers, which is equivalent to slantwise homogeneous, and vertically homogeneous layers, resulting in continuous T-S property variations across the stratification interface (e.g., van Haren and Millot (2009). By the same token, the difference in f-motions in the different layers will be differently polarized, and hence shear will change. To complicate things further, indications like variations in horizontal current polarization, changing from near-circular to increasingly elliptic, may vary strongly in the vertical, as has been shown in a numerical model (Gerkema and Exarchou, 2008). This may ‘explain’ the observed z,t-variable polarization for near-inertial horizontal motions (Fig. 9). Generally, near-f motions generate most shear because of their short vertical scales in stratified waters, especially in the Mediterranean where tides are also weak, resulting in generation of diapycnal turbulent overturning and mixing. Needless to say that the complex inertial internal wave propagation which is capable of un-attenuated border-crossing between homogeneous and stratified layers, will influence turbulent mixing in the deep. However, more future observational and modelling studies, also from other weakly stratified basins, are wanted for the precise mechanisms of deep-sea mixing that is so relevant for life in the abyss. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

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