Hostname: page-component-54dcc4c588-smtgx Total loading time: 0 Render date: 2025-09-12T00:36:25.816Z Has data issue: false hasContentIssue false
  • English
  • Français

Geophysical turbulence dominated by inertia–gravity waves

Published online by Cambridge University Press:  18 July 2019

Jim Thomas Open the ORCID record for Jim Thomas [Opens in a new window]  and
Ray Yamada
Jim Thomas*
Affiliation:
Woods Hole Oceanographic Institution, MA 02543, USA Department of Oceanography, Dalhousie University, Halifax, Canada
Ray Yamada
Affiliation:
Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: jimthomas.edu@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

JFM classification

Geophysical and Geological Flows: Geostrophic turbulence Geophysical and Geological Flows: Internal waves

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 875 , 25 September 2019 , pp. 71 - 100
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Alford, M. H., MacKinnon, J. A., Simmons, H. L. & Nash, J. D. 2016 Near-inertial internal gravity waves in the ocean. Annu. Rev. Marine Sci. 8, 95–123.Google Scholar
Babin, A., Mahalov, A. & Nicolaenko, B. 1997 Global splitting and regularity of rotating shallow-water equations. Eur. J. Mech. (B/Fluids) 16 (1), 725–754.Google Scholar
Barkan, R., Winters, K. B. & McWilliams, J. C. 2017 Stimulated imbalance and the enhancement of eddy kinetic energy dissipation by internal waves. J. Phys. Oceanogr. 47, 181–198.Google Scholar
Bartello, P. 1995 Geostrophic adjustment and inverse cascades in rotating stratified turbulence. J. Atmos. Sci. 52, 4410–4428.Google Scholar
Benavides, S. J. & Alexakis, A. 2017 Critical transitions in thin layer turbulence. J. Fluid Mech. 822, 364–385.Google Scholar
Bühler, O., Callies, J. & Ferrari, R. 2014 Wave-vortex decomposition of one-dimensional ship-track data. J. Fluid Mech. 756, 1007–1026.Google Scholar
Bühler, O. & McIntyre, M. E. 1998 On non-dissipative wave mean interactions in the atmosphere or oceans. J. Fluid Mech. 354, 301–343.Google Scholar
Callies, J., Ferrari, R. & Bühler, O. 2014 Transition from geostrophic turbulence to inertia-gravity waves in the atmospheric energy spectrum. Proc. Natl Acad. Sci. USA 111, 17033–17038.Google Scholar
Chelton, D. B., Schlax, M. G. & Samelson, R. M. 2011 Global observations of nonlinear mesoscale eddies. Prog. Oceanogr. 91, 167–216.Google Scholar
Computational and Information Systems Laboratory2017 Cheyenne: HPE/SGI ICE XA System (University Community Computing). Boulder, CO: National Center for Atmospheric Research. doi:10.5065/D6RX99HX.Google Scholar
Craik, A. D. D. & Leibovich, S. 1976 A rational model for langmuir circulations. J. Fluid Mech. 73, 401–426.Google Scholar
Davidson, P. A. 2013 Turbulence in Rotating, Stratified and Electrically Conducting Fluids. Cambridge University Press.Google Scholar
Dewar, W. K. & Killworth, P. D. 1995 Do fast gravity waves interact with geostrophic motions? Deep-Sea Res. I 42 (7), 1063–1081.Google Scholar
Dunphy, M. & Lamb, K. G. 2014 Focusing and vertical mode scattering of the first mode internal tide by mesoscale eddy interaction. J. Geophys. Res. 119, 523–536.Google Scholar
Falkovich, G. & Kritsuk, A. G. 2017 How vortices and shocks provide for a flux loop in two-dimensional compressible turbulence. Phys. Rev. Fluids 2R, 092603.Google Scholar
Falkovich, G. E. 1992 Inverse cascade and wave condensate in mesoscale atmospheric turbulence. Phys. Rev. Lett. 69, 3173–3176.Google Scholar
Falkovich, G. E. & Medvedev, S. B. 1992 Kolmogorov-like spectrum for turbulence of inertial-gravity waves. Eur. Phys. Lett. 19, 279–284.Google Scholar
Farge, M. & Sadourny, R. 1989 Wave-vortex dynamics in rotating shallow water. J. Fluid Mech. 206, 433–462.Google Scholar
Ferrari, R. & Wunsch, C. 2009 Ocean circulation kinetic energy: reservoirs, sources and sinks. Annu. Rev. Fluid Mech. 41 (1), 253–282.Google Scholar
Ferrari, R. & Wunsch, C. 2010 The distribution of eddy kinetic and potential energies in the global ocean. Tellus 62A, 92–108.Google Scholar
Francois, N., Xia, H., Punzmann, H. & Shats, M. 2013 Inverse energy cascade and emergence of large coherent vortices in turbulence driven by faraday waves. Phys. Rev. Lett. 110, 194501.Google Scholar
Frierson, D. M. W., Majda, A. J. & Pauluis, O. M. 2004 Large scale dynamics of precipitation fronts in the tropical atmosphere: a novel relaxation limit. Commun. Math. Sci. 2, 591–626.Google Scholar
Fu, L. L. & Flierl, G. R. 1980 Nonlinear energy and enstrophy transfers in a realistically stratified ocean. Dyn. Atmos. Oceans 4, 219–246.Google Scholar
Garrett, C. & Kunze, E. 2007 Internal tide generation in the deep ocean. Annu. Rev. Fluid Mech. 39, 57–87.Google Scholar
Gertz, A. & Straub, D. N. 2009 Near-inertial oscillations and the damping of midlatitude gyres: a modelling study. J. Phys. Oceanogr. 39, 2338–2350.Google Scholar
Gupta, P. & Scalo, C. 2018 Spectral energy cascade and decay in nonlinear acoustic waves. Phys. Rev. E 98, 033117.Google Scholar
Jiang, Q. & Smith, R. B. 2003 Gravity wave breaking in two-layer hydrostatic flow. J. Atmos. Sci. 60, 1159–1172.Google Scholar
Johnston, T. M. S. & Merryfield, M. A. 2003 Internal tide scattering at seamounts, ridges, and islands. J. Geophys. Res. 108 (C6), 3180.Google Scholar
Kunze, E. & Llewellyn Smith, S. G. 2004 The role of small-scale topography in the turbulent mixing of the global ocean. Oceanography 17, 55–64.Google Scholar
Kuznetsov, E. 2004 Turbulence spectra generated by singularities. J. Expl Theor. Phys. Lett. 80, 83–89.Google Scholar
Lahaye, N. & Zeitlin, V. 2012a Decaying vortex and wave turbulence in rotating shallow water model, as follows from high-resolution direct numerical simulations. Phys. Fluids 24, 115106.Google Scholar
Lahaye, N. & Zeitlin, V. 2012b 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.Google Scholar
Lamb, K. 2004 Nonlinear interaction among internal wave beams generated by tidal flow over supercritical topography. Geophys. Res. Lett. 31, L09313.Google Scholar
Leibovich, S. 1980 On wave-current interaction theories of langmuir circulations. J. Fluid Mech. 99, 715–724.Google Scholar
Lelong, M. P. & Riley, J. J. 1991 Internal wave-vortical mode interactions in strongly stratified flows. J. Fluid Mech. 232, 1–19.Google Scholar
Lindborg, E. & Mohanan, A. V. 2017 A two-dimensional toy model for geophysical turbulence. Phys. Fluids 29, 111114.Google Scholar
MacKinnon, J. A. & Winters, K. B. 2005 Subtropical catastrophe: significant loss of low-mode tidal energy at 28.9 degrees. Geophys. Res. Lett. 32, L15605.Google Scholar
Majda, A. J. 2002 Introduction to Partial Differential Equations and Waves for the Atmosphere and Ocean-Courant Lecture Notes, Bd. 9. American Mathematical Society.Google Scholar
Majda, A. J. & Embid, P. 1998 Averaging over fast gravity waves for geophysical flows with unbalanced initial data. Theor. Comput. Fluid Dyn. 11, 155–169.Google Scholar
Maltrud, M. E. & Vallis, G. K. 1993 Energy and enstrophy transfer in numerical simulations of two-dimensional turbulence. Phys. Fluids 5, 984–997.Google Scholar
McComas, C. H. & Bretherton, F. P. 1977 Resonant interaction of oceanic internal waves. J. Geophys. Res. 82, 1397–1412.Google Scholar
Murray, B. & Bustamante, M. D. 2018 Energy flux enhancement, intermittency and turbulence via fourier triad phase dynamics in the 1-d burgers equation. J. Fluid Mech. 850, 624–645.Google Scholar
Musacchio, S. & Boffetta, G. 2019 Condensate in quasi-two-dimensional turbulence. Phys. Rev. Fluids 4, 022602.Google Scholar
Nagai, T. A., Tandon, A., Kunze, E. & Mahadevan, A. 2015 Spontaneous generation of near-inertial waves by the kuroshio front. J. Phys. Oceanogr. 45, 2381–2406.Google Scholar
Pauluis, O. M., Frierson, D. M. W. & Majda, A. J. 2008 Precipitation fronts and the reflection and transmission of tropical disturbances. Q. J. R. Meteorol. Soc. 134, 913–930.Google Scholar
Polvani, L. M., McWilliams, J. C., Spall, M. A. & Ford, R. 1994 The coherent structures of shallow-water turbulence: deformation-radius effects, cyclone/anticyclone asymmetry and gravity-wave generation. Chaos 4, 177–186.Google Scholar
Ponte, A. L. & Klein, P. 2015 Incoherent signature of internal tides on sea level in idealized numerical simulations. Geophys. Res. Lett. 42, 1520–1526.Google Scholar
Pratt, L. 1983 On inertial flow over topography. Part 1. Semigeostropic adjustment to an obstacle. J. Fluid Mech. 131, 195–218.Google Scholar
Qiu, B., Chen, S., Klein, P., Wang, J., Torres, H., Fu, L. & Menemenlis, D. 2018 Seasonality in transition scale from balanced to unbalanced motions in the world ocean. J. Phys. Oceanogr. 48, 591–605.Google Scholar
Qiu, B., Nakano, T., Chen, S. & Klein, P. 2017 Submesoscale transition from geostrophic flows to internal waves in the northwestern pacific upper ocean. Nat. Commun. 8, 14055.Google Scholar
Rainville, L. & Pinkel, R. 2006 Propagation of low-mode internal waves through the ocean. J. Phys. Oceanogr. 36, 1220–1237.Google Scholar
Ray, R. D. & Mitchum, G. T. 1997 Surface manifestation of internal tides in the deep ocean: observations from altimetry and island gauges. Prog. Oceanogr. 40, 135–162.Google Scholar
Ray, R. D. & Zaron, E. D. 2016 M2 internal tides and their observed wavenumber spectra from satellite altimetry. J. Phys. Oceanogr. 46, 3–22.Google Scholar
Remmel, M. & Smith, L. 2009 New intermediate models for rotating shallow water and an investigation of the preference for anticyclones. J. Fluid Mech. 635, 321–359.Google Scholar
Richman, J. G., Arbic, B. K., Shriver, J. F., Metzger, E. J. & Wallcraft, A. J. 2012 Inferring dynamics from the wavenumber spectra of an eddying global ocean model with embedded tides. J. Geophys. Res. 117, C12012.Google Scholar
Rocha, C. B., Chereskin, T. K., Gille, S. T. & Menemenlis, D. 2016 Mesoscale to submesoscale wavenumber spectra in drake passage. J. Phys. Oceanogr. 46, 601–620.Google Scholar
Rocha, C. B., Wagner, G. L. & Young, W. R. 2018 Stimulated generation-extraction of energy from balanced flow by near-inertial waves. J. Fluid Mech. 847, 417–451.Google Scholar
Salmon, R. 1978 Lectures on Geophysical Fluid Dynamics. Oxford University Press.Google Scholar
Smith, K. S. & Vallis, G. K. 2001 The scales and equilibration of midocean eddies: freely evolving flow. J. Phys. Oceanogr. 31, 554–571.Google Scholar
Spyksma, K., Magcalas, M. & Campbell, N. 2012 Quantifying effects of hyperviscosity on isotropic turbulence. Phys. Fluids 24, 125102.Google Scholar
Stechmann, S. N. & Majda, A. J. 2006 The structure of precipitation fronts for finite relaxation time. Theor. Comput. Fluid Dyn. 20, 377–404.Google Scholar
Sutherland, B. 2016 Excitation of superharmonics by internal modes in a non-uniformly stratified fluid. J. Fluid Mech. 793, 335–352.Google Scholar
Taylor, S. & Straub, D. 2016 Forced near-inertial motion and dissipation of low-frequency kinetic energy in a wind-driven channel flow. J. Phys. Oceanogr. 46, 79–93.Google Scholar
Thomas, J. 2016 Resonant fast-slow interactions and breakdown of quasi-geostrophy in rotating shallow water. J. Fluid Mech. 788, 492–520.Google Scholar
Thomas, J., Bühler, O. & Smith, K. S. 2018 Wave-induced mean flows in rotating shallow water with uniform potential vorticity. J. Fluid Mech. 839, 408–429.Google Scholar
Thomas, L. N. 2017 On the modifications of near-inertial waves at fronts: implications for energy transfer across scales. Ocean Dyn. 67, 1335–1350.Google Scholar
Thomas, L. N. & Taylor, J. R. 2014 Damping of inertial motions by parametric subharmonic instability in baroclinic currents. J. Fluid Mech. 743, 280–294.Google Scholar
Vallis, G. K. 2006 Atmospheric and Oceanic Fluid Dynamics. Cambridge University Press.Google Scholar
Wagner, G. L. & Young, W. R. 2015 Available potential vorticity and wave-averaged quasi-geostrophic flow. J. Fluid Mech. 785, 401–424.Google Scholar
Wagner, G. L. & Young, W. R. 2016 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.Google Scholar
Waite, M. L. 2017 Random forcing of geostrophic motion in rotating stratified turbulence. Phys. Fluid 29, 126602.Google Scholar
Waite, M. L. & Bartello, P. 2006 The transition from geostrophic to stratified turbulence. J. Fluid Mech. 568, 89–108.Google Scholar
Ward, M. L. & Dewar, W. K. 2010 Scattering of gravity waves by potential vorticity in a shallow-water fluid. J. Fluid Mech. 663, 478–506.Google Scholar
Whitham, G. B. 2011 Linear and Nonlinear Waves. John Wiley and Sons.Google Scholar
Wunsch, C. 1997 The vertical partition of oceanic horizontal kinetic energy and the spectrum of global variability. J. Phys. Oceanogr. 27, 1770–1794.Google Scholar
Wunsch, C. & Stammer, D. 1998 Satellite altimetry, the marine geoid and the oceanic general circulation. Annu. Rev. Earth Planet. Sci. 26, 219–254.Google Scholar
Wunsch, S. 2017 Harmonic generation by nonlinear self-interaction of a single internal wave mode. J. Fluid Mech. 828, 630–647.Google Scholar
Xie, J. H. & Vanneste, J. 2015 A generalised-lagrangian-mean model of the interactions between near-inertial waves and mean flow. J. Fluid Mech. 774, 143–169.Google Scholar
Zeitlin, V. 2018 Geophysical Fluid Dynamics: Understanding (almost) Everything with Rotating Shallow Water Models. Oxford University Press.Google Scholar
Zeitlin, V., Reznik, G. M. & Ben Jelloul 2003 Nonlinear theory of geostrophic adjustment. Part 2. Two-layer and continuously stratified primitive equations. J. Fluid Mech. 491, 207–228.Google Scholar
Zhao, Z., Alford, M. H., Girton, J., Rainville, L. & Simmons, H. 2016 Global observations of open-ocean mode-1 M 2 internal tides. J. Phys. Oceanogr. 46, 1657–1684.Google Scholar
Zhao, Z., Alford, M. H. & Girton, J. B. 2012 Mapping low-mode internal tides from multisatellite altimetry. Oceanography 25, 42–51.Google Scholar