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Geophysical turbulence dominated by inertia-gravity waves. (English) Zbl 1419.86017
Summary: Recent evidence from both oceanic observations and global-scale ocean model simulations indicate the existence of regions where low-mode internal tidal energy dominates over that of the geostrophic balanced flow. Inspired by these findings, we examine the effect of the first vertical mode inertia-gravity waves on the dynamics of balanced flow using an idealized model obtained by truncating the hydrostatic Boussinesq equations on to the barotropic and the first baroclinic mode. On investigating the wave-balance turbulence phenomenology using freely evolving numerical simulations, we find that the waves continuously transfer energy to the balanced flow in regimes where the balanced-to-wave energy ratio is small, thereby generating small-scale features in the balanced fields. We examine the detailed energy transfer pathways in wave-dominated flows and thereby develop a generalized small Rossby number geophysical turbulence phenomenology, with the two-mode (barotropic and one baroclinic mode) quasi-geostrophic turbulence phenomenology being a subset of it. The present work therefore shows that inertia-gravity waves would form an integral part of the geophysical turbulence phenomenology in regions where balanced flow is weaker than gravity waves.

86A05 Hydrology, hydrography, oceanography
76U05 General theory of rotating fluids
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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[1] Alford, M. H.; Mackinnon, J. A.; Simmons, H. L.; Nash, J. D., Near-inertial internal gravity waves in the ocean, Annu. Rev. Marine Sci., 8, 95-123, (2016)
[2] Babin, A.; Mahalov, A.; Nicolaenko, B., Global splitting and regularity of rotating shallow-water equations, Eur. J. Mech. (B/Fluids), 16, 1, 725-754, (1997) · Zbl 0889.76007
[3] Barkan, R.; Winters, K. B.; Mcwilliams, J. C., Stimulated imbalance and the enhancement of eddy kinetic energy dissipation by internal waves, J. Phys. Oceanogr., 47, 181-198, (2017)
[4] Bartello, P., Geostrophic adjustment and inverse cascades in rotating stratified turbulence, J. Atmos. Sci., 52, 4410-4428, (1995)
[5] Benavides, S. J.; Alexakis, A., Critical transitions in thin layer turbulence, J. Fluid Mech., 822, 364-385, (2017) · Zbl 1387.86026
[6] Bühler, O.; Callies, J.; Ferrari, R., Wave-vortex decomposition of one-dimensional ship-track data, J. Fluid Mech., 756, 1007-1026, (2014) · Zbl 1327.86004
[7] Bühler, O.; Mcintyre, M. E., On non-dissipative wave mean interactions in the atmosphere or oceans, J. Fluid Mech., 354, 301-343, (1998) · Zbl 0922.76281
[8] Callies, J.; Ferrari, R.; Bühler, O., Transition from geostrophic turbulence to inertia-gravity waves in the atmospheric energy spectrum, Proc. Natl Acad. Sci. USA, 111, 17033-17038, (2014)
[9] Chelton, D. B.; Schlax, M. G.; Samelson, R. M., Global observations of nonlinear mesoscale eddies, Prog. Oceanogr., 91, 167-216, (2011)
[10] 2017 Cheyenne: HPE/SGI ICE XA System (University Community Computing). Boulder, CO: National Center for Atmospheric Research. doi:10.5065/D6RX99HX.
[11] Craik, A. D. D.; Leibovich, S., A rational model for langmuir circulations, J. Fluid Mech., 73, 401-426, (1976) · Zbl 0324.76014
[12] Davidson, P. A., Turbulence in Rotating, Stratified and Electrically Conducting Fluids, (2013), Cambridge University Press · Zbl 1282.76001
[13] Dewar, W. K.; Killworth, P. D., Do fast gravity waves interact with geostrophic motions?, Deep-Sea Res. I, 42, 7, 1063-1081, (1995)
[14] Dunphy, M.; Lamb, K. G., Focusing and vertical mode scattering of the first mode internal tide by mesoscale eddy interaction, J. Geophys. Res., 119, 523-536, (2014)
[15] Falkovich, G.; Kritsuk, A. G., How vortices and shocks provide for a flux loop in two-dimensional compressible turbulence, Phys. Rev. Fluids, 2R, (2017)
[16] Falkovich, G. E., Inverse cascade and wave condensate in mesoscale atmospheric turbulence, Phys. Rev. Lett., 69, 3173-3176, (1992)
[17] Falkovich, G. E.; Medvedev, S. B., Kolmogorov-like spectrum for turbulence of inertial-gravity waves, Eur. Phys. Lett., 19, 279-284, (1992)
[18] Farge, M.; Sadourny, R., Wave-vortex dynamics in rotating shallow water, J. Fluid Mech., 206, 433-462, (1989) · Zbl 0678.76011
[19] Ferrari, R.; Wunsch, C., Ocean circulation kinetic energy: reservoirs, sources and sinks, Annu. Rev. Fluid Mech., 41, 1, 253-282, (2009) · Zbl 1159.76050
[20] Ferrari, R.; Wunsch, C., The distribution of eddy kinetic and potential energies in the global ocean, Tellus, 62A, 92-108, (2010)
[21] Francois, N.; Xia, H.; Punzmann, H.; Shats, M., Inverse energy cascade and emergence of large coherent vortices in turbulence driven by faraday waves, Phys. Rev. Lett., 110, (2013)
[22] Frierson, D. M. W.; Majda, A. J.; Pauluis, O. M., Large scale dynamics of precipitation fronts in the tropical atmosphere: a novel relaxation limit, Commun. Math. Sci., 2, 591-626, (2004) · Zbl 1160.86303
[23] Fu, L. L.; Flierl, G. R., Nonlinear energy and enstrophy transfers in a realistically stratified ocean, Dyn. Atmos. Oceans, 4, 219-246, (1980)
[24] Garrett, C.; Kunze, E., Internal tide generation in the deep ocean, Annu. Rev. Fluid Mech., 39, 57-87, (2007) · Zbl 1296.76026
[25] Gertz, A.; Straub, D. N., Near-inertial oscillations and the damping of midlatitude gyres: a modelling study, J. Phys. Oceanogr., 39, 2338-2350, (2009)
[26] Gupta, P.; Scalo, C., Spectral energy cascade and decay in nonlinear acoustic waves, Phys. Rev. E, 98, (2018)
[27] Jiang, Q.; Smith, R. B., Gravity wave breaking in two-layer hydrostatic flow, J. Atmos. Sci., 60, 1159-1172, (2003)
[28] Johnston, T. M. S.; Merryfield, M. A., Internal tide scattering at seamounts, ridges, and islands, J. Geophys. Res., 108, C6, 3180, (2003)
[29] Kunze, E.; Llewellyn Smith, S. G., The role of small-scale topography in the turbulent mixing of the global ocean, Oceanography, 17, 55-64, (2004)
[30] Kuznetsov, E., Turbulence spectra generated by singularities, J. Expl Theor. Phys. Lett., 80, 83-89, (2004)
[31] Lahaye, N.; Zeitlin, V., Decaying vortex and wave turbulence in rotating shallow water model, as follows from high-resolution direct numerical simulations, Phys. Fluids, 24, (2012)
[32] Lahaye, N.; Zeitlin, V., Existence and properties of ageostrophic modons and coherent tripoles in the two-layer rotating shallow water model on the f-plane, J. Fluid Mech., 706, 71-107, (2012) · Zbl 1275.76217
[33] Lamb, K., Nonlinear interaction among internal wave beams generated by tidal flow over supercritical topography, Geophys. Res. Lett., 31, L09313, (2004)
[34] Leibovich, S., On wave-current interaction theories of langmuir circulations, J. Fluid Mech., 99, 715-724, (1980) · Zbl 0452.76013
[35] Lelong, M. P.; Riley, J. J., Internal wave-vortical mode interactions in strongly stratified flows, J. Fluid Mech., 232, 1-19, (1991) · Zbl 0737.76012
[36] Lindborg, E.; Mohanan, A. V., A two-dimensional toy model for geophysical turbulence, Phys. Fluids, 29, (2017)
[37] Mackinnon, J. A.; Winters, K. B., Subtropical catastrophe: significant loss of low-mode tidal energy at 28.9 degrees, Geophys. Res. Lett., 32, L15605, (2005)
[38] Majda, A. J., Introduction to Partial Differential Equations and Waves for the Atmosphere and Ocean-Courant Lecture Notes, Bd. 9, (2002), American Mathematical Society
[39] Majda, A. J.; Embid, P., Averaging over fast gravity waves for geophysical flows with unbalanced initial data, Theor. Comput. Fluid Dyn., 11, 155-169, (1998) · Zbl 0923.76339
[40] Maltrud, M. E.; Vallis, G. K., Energy and enstrophy transfer in numerical simulations of two-dimensional turbulence, Phys. Fluids, 5, 984-997, (1993)
[41] Mccomas, C. H.; Bretherton, F. P., Resonant interaction of oceanic internal waves, J. Geophys. Res., 82, 1397-1412, (1977)
[42] Murray, B.; Bustamante, M. D., Energy flux enhancement, intermittency and turbulence via fourier triad phase dynamics in the 1-d burgers equation, J. Fluid Mech., 850, 624-645, (2018) · Zbl 1415.76251
[43] Musacchio, S.; Boffetta, G., Condensate in quasi-two-dimensional turbulence, Phys. Rev. Fluids, 4, (2019) · Zbl 1184.76063
[44] Nagai, T. A.; Tandon, A.; Kunze, E.; Mahadevan, A., Spontaneous generation of near-inertial waves by the kuroshio front, J. Phys. Oceanogr., 45, 2381-2406, (2015)
[45] Pauluis, O. M.; Frierson, D. M. W.; Majda, A. J., Precipitation fronts and the reflection and transmission of tropical disturbances, Q. J. R. Meteorol. Soc., 134, 913-930, (2008)
[46] Polvani, L. M.; Mcwilliams, J. C.; Spall, M. A.; Ford, R., The coherent structures of shallow-water turbulence: deformation-radius effects, cyclone/anticyclone asymmetry and gravity-wave generation, Chaos, 4, 177-186, (1994)
[47] Ponte, A. L.; Klein, P., Incoherent signature of internal tides on sea level in idealized numerical simulations, Geophys. Res. Lett., 42, 1520-1526, (2015)
[48] Pratt, L., On inertial flow over topography. Part 1. Semigeostropic adjustment to an obstacle, J. Fluid Mech., 131, 195-218, (1983) · Zbl 0533.76045
[49] Qiu, B.; Chen, S.; Klein, P.; Wang, J.; Torres, H.; Fu, L.; Menemenlis, D., Seasonality in transition scale from balanced to unbalanced motions in the world ocean, J. Phys. Oceanogr., 48, 591-605, (2018)
[50] Qiu, B.; Nakano, T.; Chen, S.; Klein, P., Submesoscale transition from geostrophic flows to internal waves in the northwestern pacific upper ocean, Nat. Commun., 8, (2017)
[51] Rainville, L.; Pinkel, R., Propagation of low-mode internal waves through the ocean, J. Phys. Oceanogr., 36, 1220-1237, (2006)
[52] Ray, R. D.; Mitchum, G. T., Surface manifestation of internal tides in the deep ocean: observations from altimetry and island gauges, Prog. Oceanogr., 40, 135-162, (1997)
[53] Ray, R. D.; Zaron, E. D., M_{2} internal tides and their observed wavenumber spectra from satellite altimetry, J. Phys. Oceanogr., 46, 3-22, (2016)
[54] Remmel, M.; Smith, L., New intermediate models for rotating shallow water and an investigation of the preference for anticyclones, J. Fluid Mech., 635, 321-359, (2009) · Zbl 1183.76641
[55] Richman, J. G.; Arbic, B. K.; Shriver, J. F.; Metzger, E. J.; Wallcraft, A. J., Inferring dynamics from the wavenumber spectra of an eddying global ocean model with embedded tides, J. Geophys. Res., 117, C12012, (2012)
[56] Rocha, C. B.; Chereskin, T. K.; Gille, S. T.; Menemenlis, D., Mesoscale to submesoscale wavenumber spectra in drake passage, J. Phys. Oceanogr., 46, 601-620, (2016)
[57] Rocha, C. B.; Wagner, G. L.; Young, W. R., Stimulated generation-extraction of energy from balanced flow by near-inertial waves, J. Fluid Mech., 847, 417-451, (2018) · Zbl 1404.76068
[58] Salmon, R., Lectures on Geophysical Fluid Dynamics, (1978), Oxford University Press
[59] Smith, K. S.; Vallis, G. K., The scales and equilibration of midocean eddies: freely evolving flow, J. Phys. Oceanogr., 31, 554-571, (2001)
[60] Spyksma, K.; Magcalas, M.; Campbell, N., Quantifying effects of hyperviscosity on isotropic turbulence, Phys. Fluids, 24, (2012)
[61] Stechmann, S. N.; Majda, A. J., The structure of precipitation fronts for finite relaxation time, Theor. Comput. Fluid Dyn., 20, 377-404, (2006)
[62] Sutherland, B., Excitation of superharmonics by internal modes in a non-uniformly stratified fluid, J. Fluid Mech., 793, 335-352, (2016) · Zbl 1382.76035
[63] Taylor, S.; Straub, D., Forced near-inertial motion and dissipation of low-frequency kinetic energy in a wind-driven channel flow, J. Phys. Oceanogr., 46, 79-93, (2016)
[64] Thomas, J., Resonant fast-slow interactions and breakdown of quasi-geostrophy in rotating shallow water, J. Fluid Mech., 788, 492-520, (2016) · Zbl 1381.76390
[65] Thomas, J.; Bühler, O.; Smith, K. S., Wave-induced mean flows in rotating shallow water with uniform potential vorticity, J. Fluid Mech., 839, 408-429, (2018) · Zbl 1419.86016
[66] Thomas, L. N., On the modifications of near-inertial waves at fronts: implications for energy transfer across scales, Ocean Dyn., 67, 1335-1350, (2017)
[67] Thomas, L. N.; Taylor, J. R., Damping of inertial motions by parametric subharmonic instability in baroclinic currents, J. Fluid Mech., 743, 280-294, (2014)
[68] Vallis, G. K., Atmospheric and Oceanic Fluid Dynamics, (2006), Cambridge University Press
[69] Wagner, G. L.; Young, W. R., Available potential vorticity and wave-averaged quasi-geostrophic flow, J. Fluid Mech., 785, 401-424, (2015) · Zbl 1381.86018
[70] Wagner, G. L.; Young, W. R., A three-component model for the coupled evolution of near-inertial waves, quasi-geostrophic flow and the near-inertial second harmonic, J. Fluid Mech., 802, 806-837, (2016) · Zbl 1456.76036
[71] Waite, M. L., Random forcing of geostrophic motion in rotating stratified turbulence, Phys. Fluid, 29, (2017)
[72] Waite, M. L.; Bartello, P., The transition from geostrophic to stratified turbulence, J. Fluid Mech., 568, 89-108, (2006) · Zbl 1177.76147
[73] Ward, M. L.; Dewar, W. K., Scattering of gravity waves by potential vorticity in a shallow-water fluid, J. Fluid Mech., 663, 478-506, (2010) · Zbl 1205.76065
[74] Whitham, G. B., Linear and Nonlinear Waves, (2011), John Wiley and Sons · Zbl 0373.76001
[75] Wunsch, C., The vertical partition of oceanic horizontal kinetic energy and the spectrum of global variability, J. Phys. Oceanogr., 27, 1770-1794, (1997)
[76] Wunsch, C.; Stammer, D., Satellite altimetry, the marine geoid and the oceanic general circulation, Annu. Rev. Earth Planet. Sci., 26, 219-254, (1998)
[77] Wunsch, S., Harmonic generation by nonlinear self-interaction of a single internal wave mode, J. Fluid Mech., 828, 630-647, (2017)
[78] Xie, J. H.; Vanneste, J., A generalised-lagrangian-mean model of the interactions between near-inertial waves and mean flow, J. Fluid Mech., 774, 143-169, (2015) · Zbl 1328.76055
[79] Zeitlin, V., Geophysical Fluid Dynamics: Understanding (almost) Everything with Rotating Shallow Water Models, (2018), Oxford University Press · Zbl 1382.86001
[80] Zeitlin, V.; Reznik, G. M.; , Nonlinear theory of geostrophic adjustment. Part 2. Two-layer and continuously stratified primitive equations, J. Fluid Mech., 491, 207-228, (2003) · Zbl 1063.76010
[81] Zhao, Z.; Alford, M. H.; Girton, J.; Rainville, L.; Simmons, H., Global observations of open-ocean mode-1 M_{2} internal tides, J. Phys. Oceanogr., 46, 1657-1684, (2016)
[82] Zhao, Z.; Alford, M. H.; Girton, J. B., Mapping low-mode internal tides from multisatellite altimetry, Oceanography, 25, 42-51, (2012)
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