Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-02T18:52:00.920Z Has data issue: false hasContentIssue false
  • English
  • Français

Forward flux and enhanced dissipation of geostrophic balanced energy

Published online by Cambridge University Press:  03 February 2021

Jim Thomas Open the ORCID record for Jim Thomas [Opens in a new window]  and
Don Daniel
Jim Thomas*
Affiliation:
Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC27599, USA
Don Daniel
Affiliation:
Los Alamos National Laboratory, New Mexico, NM87545, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A broad spectrum of internal gravity waves coexist with the geostrophic balanced flow in the world's oceans. Satellite altimeter data sets, in situ observations and global scale ocean model outputs collected over the past one decade reveal significant variability in the balance-to-wave energy ratio in the world's oceans. Notably, wave-dominant regions of the world's oceans are characterized by the internal gravity wave spectrum overtaking the geostrophic balanced flow's spectrum at mesoscales. Inspired by these recent data sets, in this paper we explore turbulent interactions between a broad spectrum of internal gravity waves and the geostrophic balanced flow in different balance-to-wave energy regimes. Our results based on numerical integration of the non-hydrostatic Boussinesq equations reveal that the balanced flow remains unaffected by waves as long as wave energy is not significantly higher than balanced energy. Even in parameter regimes where wave and balanced energies are comparable, balanced flow undergoes an inverse energy flux with energy accumulating in large domain-scale coherent vortices. In contrast, we find that wave-dominant regimes are composed of two-way wave–balance energy exchanges and a forward flux of geostrophic energy. The geostrophic balanced flow in such regimes is composed of fine-scale structures that get dissipated at small scales and show no sign of coherent vortex formation. Our findings reveal that sufficiently high energy waves can reverse the direction of the geostrophic energy flux – from inverse to forward – enhancing geostrophic energy dissipation. Given that the balance-to-wave energy ratio is highly variable in the global ocean, the forward flux and associated small-scale dissipation of balanced energy could play an important role in high wave energy regions of the world's oceans. The prominent mechanisms suggested for dissipating balanced energy in the world's oceans require balanced flow to encounter different forms of boundaries. In contrast, the wave-induced dissipation of balanced energy described in this paper is an attractive mechanism that could dissipate balanced energy in the interior parts of the oceans and away from all forms of boundaries.

JFM classification

Geophysical and Geological Flows: Geostrophic turbulence Geophysical and Geological Flows: Internal waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 911 , 25 March 2021 , A60
Check for updates
Copyright
© The Author(s), 2021. Published by 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.)

References

REFERENCES

Alexakis, A. & Biferale, L. 2018 Cascades and transitions in turbulent flows. Phys. Rep. 767–769, 1–101.CrossRefGoogle Scholar
Alford, M.H, MacKinnon, J.A., Simmons, H.L. & Nash, J.D. 2016 Near-inertial internal gravity waves in the ocean. Annu. Rev. Mar. Sci. 8, 95–123.CrossRefGoogle ScholarPubMed
Arbic, B., et al. . 2009 Estimates of bottom flows and bottom boundary layer dissipation of the oceanic general circulation from global high-resolution models. J. Geophys. Res. 114, C02024.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.CrossRefGoogle Scholar
Bartello, P. 1995 Geostrophic adjustment and inverse cascades in rotating stratified turbulence. J. Atmos. Sci. 52, 4410–4428.2.0.CO;2>CrossRefGoogle Scholar
Bühler, O., Callies, J. & Ferrari, R. 2014 Wave-vortex decomposition of one-dimensional ship-track data. J. Fluid Mech. 756, 1007–1026.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
Chelton, D.B., Schlax, M.G. & Samelson, R.M. 2011 Global observations of nonlinear mesoscale eddies. Prog. Oceanogr. 91, 167–216.CrossRefGoogle Scholar
Garrett, C. & Kunze, E. 2007 Internal tide generation in the deep ocean. Annu. Rev. Fluid Mech. 39, 57–87.CrossRefGoogle Scholar
Herbert, C., Marino, R., Rosenberg, D. & Pouquet, A. 2016 Waves and vortices in the inverse cascade regime of stratified turbulence with or without rotation. J. Fluid Mech. 806, 165–204.CrossRefGoogle Scholar
Hernandez-Duenas, G., Smith, L.M. & Stechmann, S.N. 2014 Investigation of boussinesq dynamics using intermediate models based on wave – vortical interactions. J. Fluid Mech. 747, 247–287.CrossRefGoogle Scholar
Lien, R.-C. & Sanford, T.B. 2019 Small-scale potential vorticity in the upper ocean thermocline. J. Phys. Oceanogr. 49, 1845–1872.CrossRefGoogle Scholar
MacKinnon, J.A., et al. . 2017 Climate process team on internal-wave driven ocean mixing. Bull. Am. Meteorol. Soc. 98, 2429–2454.CrossRefGoogle Scholar
McWilliams, J.C. 1989 Statistical properties of decaying geostrophic turbulence. J. Fluid Mech. 198, 199–230.CrossRefGoogle Scholar
Munk, W. & Wunsch, C. 1998 Abyssal recipes II: energetics of tidal and wind mixing. Deep-Sea Res. I 45, 1977–2010.CrossRefGoogle Scholar
Nadiga, B.T. 2014 Nonlinear evolution of a baroclinic wave and imbalanced dissipation. J. Fluid Mech. 756, 965–1006.CrossRefGoogle Scholar
Nikurashin, M., Vallis, G.K. & Adcroft, A. 2013 Routes to energy dissipation for geostrophic flows in the southern ocean. Nat. Geosci. 6, 48–51.CrossRefGoogle Scholar
Pouquet, A., Rosenberg, D., Stawarz, J.E. & Marino, R. 2019 Helicity dynamics, inverse, and bidirectional cascades in fluid and magnetohydrodynamic turbulence: a brief review. Earth Space Sci. 6, 351–369.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle 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.CrossRefGoogle Scholar
Sagaut, P. 2005 Large Eddy Simulation for Incompressible Flows: An Introduction. Springer.Google Scholar
Savage, A.C., et al. . 2017 Spectral decomposition of internal gravity wave sea surface height in global models. J. Geophys. Res.: Oceans 122, 7803–7821.CrossRefGoogle Scholar
Sen, A., Scott, R.B. & Arbic, B.K. 2013 Global energy dissipation rate of deep-ocean low-frequency flows by quadratic bottom boundary layer drag: comparisons from current-meter data. Geophys. Res. Lett. 35, L09606.Google Scholar
Shakespeare, C.J. & Hogg, A.M. 2018 The life cycle of spontaneously generated internal waves. J. Phys. Oceanogr. 48, 343–359.CrossRefGoogle Scholar
Smith, K.S. & Vallis, G.K. 2001 The scales and equilibration of midocean eddies: freely evolving flow. J. Phys. Oceanogr. 31, 554–571.2.0.CO;2>CrossRefGoogle Scholar
Smith, L.M. & Waleffe, F. 2002 Generation of slow large scales in forced rotating stratified turbulence. J. Fluid Mech. 451, 145–168.CrossRefGoogle Scholar
Stammer, D. 1997 Global characteristics of ocean variability estimated from regional topex/poseidon altimeter measurements. J. Phys. Oceanogr. 27, 1743–1769.2.0.CO;2>CrossRefGoogle 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.CrossRefGoogle Scholar
Tchilibou, M., Gourdeau, L., Morrow, R., Serazin, G., Djath, B. & Lyard, F. 2018 Spectral signatures of the tropical pacific dynamics from model and altimetry: a focus on the meso/submesoscale range. Ocean Sci. 14, 1283–1301.CrossRefGoogle Scholar
Thomas, J. & Arun, S. 2020 Near-inertial waves and geostrophic turbulence. Phys. Rev. Fluids 5, 014801.CrossRefGoogle 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.CrossRefGoogle Scholar
Thomas, J. & Daniel, D. 2020 Turbulent exchanges between near-inertial waves and balanced flows. J. Fluid Mech. 902, A7.CrossRefGoogle Scholar
Thomas, J. & Yamada, R. 2019 Geophysical turbulence dominated by inertia-gravity waves. J. Fluid Mech. 875, 71–100.CrossRefGoogle 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.CrossRefGoogle Scholar
Torres, H.S., Klein, P., Menemenlis, D., Qiu, B., Su, Z., Wang, J., Chen, S. & Fu, L.-L. 2018 Partitioning ocean motions into balanced motions and internal gravity waves: a modeling study in anticipation of future space missions. J. Geophys. Res.: Oceans 123, 8084–8105.CrossRefGoogle Scholar
Wagner, G.L. & Young, W.R. 2015 Available potential vorticity and wave-averaged quasi-geostrophic flow. J. Fluid Mech. 785, 401–424.CrossRefGoogle 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.CrossRefGoogle Scholar
Whalen, C., MacKinnon, J.A. & Talley, L.D. 2018 Large-scale impacts of the mesoscale environment on mixing from wind-driven internal waves. Nat. Geosci. 11, 842–847.CrossRefGoogle Scholar
Whalen, C., Talley, L.D. & MacKinnon, J.A. 2012 Spatial and temporal variability of global ocean mixing inferred from argo profiles. Geophys. Res. Lett. 39, L18612.CrossRefGoogle Scholar
Whalen, C.B., et al. . 2020 Internal wave-driven mixing: governing processes and consequences for climate. Nat. Rev. Earth Environ. 1, 606–621.CrossRefGoogle Scholar
Whitt, D.B. & Thomas, L.N. 2015 Resonant generation and energetics of wind-forced near-inertial motions in a geostrophic flow. J. Phys. Oceanogr. 45, 181–208.CrossRefGoogle Scholar
Wunsch, C. 1997 The vertical partition of oceanic horizontal kinetic energy and the spectrum of global variability. J. Phys. Oceanogr. 27, 1770–1794.2.0.CO;2>CrossRefGoogle Scholar
Wunsch, C. & Ferrari, R. 2004 Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech. 36, 281–314.CrossRefGoogle Scholar
Wunsch, C. & Stammer, D. 1998 Satellite altimetry, the marine geoid and the oceanic general circulation. Annu. Rev. Earth Planet. Sci. 26, 219–254.CrossRefGoogle 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.CrossRefGoogle Scholar
Xie, J.-H. 2020 Downscale transfer of quasigeostrophic energy catalyzed by near-inertial waves. J. Fluid Mech. 904, A40.CrossRefGoogle Scholar
Zhai, X., Johnson, H.L. & Marshall, D.P. 2010 Significant sink of ocean-eddy energy near western boundaries. Nat. Geosci. 3, 608–612.CrossRefGoogle Scholar