Hostname: page-component-77f85d65b8-g4pgd Total loading time: 0 Render date: 2026-04-13T16:51:35.141Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent exchanges between near-inertial waves and balanced flows

Published online by Cambridge University Press:  04 September 2020

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, North Carolina27599, USA
Don Daniel
Affiliation:
Los Alamos National Laboratory, New Mexico87545, USA
*
†Email address for correspondence: jimthomas.edu@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

Wind generated near-inertial waves are ubiquitous in the upper ocean. An improved understanding of near-inertial wave dynamics following their excitation in the ocean and their subsequent interaction with mesoscale geostrophic balanced flows is key to decoding oceanic energy flow pathways. In this regard, multiple oceanic data sets accumulated over the past few decades reveal that the relative strength of near-inertial waves and geostrophic balanced eddy fields is highly variable, both geographically and seasonally. Inspired by these observations, we investigate turbulent interactions and energy exchanges between near-inertial waves and balanced flows using freely evolving numerical simulations of the non-hydrostatic Boussinesq equations. We find accelerated vertical propagation and dissipation of the waves in regimes where balanced and wave fields have comparable strengths. In such regimes we also find that near-inertial waves directly extract energy from balanced flows, with $O(10\, \%)$ being the amount of balanced energy loss. In contrast, we find that near-inertial waves transfer energy to balanced flows in regimes where balance-to-wave energy ratio is small, with the gain in balanced energy being dependent on the relative strength of waves. Furthermore, these regimes are characterized by relatively weaker vertical propagation and dissipation of the near-inertial wave field. One of the key outcomes of this study is the demonstration of the lack of a unique direction for near-inertial wave-balanced flow energy transfers. Depending on the balance-to-wave energy ratio, near-inertial waves can act as an energy sink or energy source for the geostrophic balanced flow.

JFM classification

Geophysical and Geological Flows: Air/sea interactions Geophysical and Geological Flows: Ocean processes

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 902 , 10 November 2020 , A7
Check for updates
Copyright
© The Author(s), 2020. 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.)

Article purchase

Temporarily unavailable

References

REFERENCES

Alford, M. H. 2003 a Energy available for ocean mixing redistributed through long-range propagation of internal waves. Nature 423, 159–163.CrossRefGoogle Scholar
Alford, M. H. 2003 b Improved global maps and 54-year history of wind-work on ocean inertial motions. Geophys. Res. Lett. 30, 1424.Google 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
Alford, M. H. & Whitmont, M. 2007 Seasonal and spatial variability of near-inertial kinetic energy from historical moored velocity records. J. Phys. Oceanogr. 37, 2022–2037.CrossRefGoogle Scholar
Arbic, B. K., Shriver, J. F., Hogan, P. J., Hurlburt, H. E., McClean, J. L., Metzger, E. J., Scott, R. B., Sen, A., Smedstad, O. M. & Wallcraft, A. J., 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.CrossRefGoogle Scholar
Asselin, O. & Young, W. R. 2019 An improved model of near-inertial wave dynamics. J. Fluid Mech. 876, 428–448.CrossRefGoogle Scholar
Balmforth, N. J., Llewellyn Smith, S. G. & Young, W. R. 1998 Enhanced dispersion of near-inertial waves in an idealized geostrophic flow. J. Mar. Res. 56, 1–40.CrossRefGoogle 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
Chaigneau, A., Pizarro, O. & Rojas, W. 2008 Global climatology of near-inertial current characteristics from Lagrangian observations. Geophys. Res. Lett. 35, L13603.CrossRefGoogle Scholar
Danioux, E., Klein, P. & Riviere, P. 2008 Propagation of wind energy into the deep ocean through a fully turbulent mesoscale eddy field. J. Phys. Oceanogr. 38, 2224–2241.CrossRefGoogle Scholar
Danioux, E., Vanneste, J. & Bühler, O. 2015 On the concentration of near-inertial waves in anticyclones. J. Fluid Mech. 773, R2.CrossRefGoogle Scholar
D'Asaro, E. A., Eriksen, C. C., Levine, M. A., Niiler, P., Paulson, C. A. & van Meurs, P. 1995 Upper ocean inertial currents forced by a strong storm. Part I: data and comparisons with linear theory. J. Phys. Oceanogr. 25, 2909–2936.2.0.CO;2>CrossRefGoogle Scholar
Deusebio, E., Vallgren, A. & Lindborg, E. 2013 The route to dissipation in strongly stratified and rotating flows. J. Fluid Mech. 720, 66–103.CrossRefGoogle Scholar
Elipot, S., Lumpkin, R. & Prieto, G. 2010 Modification of inertial oscillations by the mesoscale eddy field. J. Geophys. Res. 115, C09010.CrossRefGoogle Scholar
Embid, P. & Majda, A. J. 1998 Low froude number limiting dynamics for stably stratified flow with small or finite Rossby numbers. Geophys. Astrophys. Fluid Dyn. 87, 1–50.CrossRefGoogle Scholar
Ferrari, R. & Wunsch, C. 2009 Ocean circulation kinetic energy: reservoirs, sources and sinks. Annu. Rev. Fluid Mech. 41 (1), 253–282.CrossRefGoogle 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.CrossRefGoogle Scholar
Grisouard, N. & Thomas, L. N. 2015 Energy exchanges between density fronts and near-inertial waves reflecting off the ocean surface. J. Phys. Oceanogr. 46, 501–516.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
Hogg, A., Dewar, W. K., Berloff, P. & Ward, M. L. 2011 Kelvin wave hydraulic control induced by interactions between vortices and topography. J. Fluid Mech. 687, 194–208.CrossRefGoogle Scholar
Joyce, T. M., Toole, J. M., Klein, P. & Thomas, L. N. 2013 A near-inertial mode observed within a gulf stream warm-core ring. J. Geophys. Res. 118, 1797–1806.CrossRefGoogle Scholar
Kunze, E. 1985 Near-inertial wave propagation in geostrophic shear. J. Phys. Oceanogr. 15, 544–565.2.0.CO;2>CrossRefGoogle Scholar
Lee, D.-K. & Niiler, P. P. 1998 The inertial chimney: the near-inertial energy drainage from the ocean surface to the deep layer. J. Geophys. Res. 103 (C4), 7579–7591.CrossRefGoogle 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
Munk, W. & Wunsch, C. 1998 Abyssal recipes II: energetics of tidal and wind mixing. Deep-Sea Res. I 45, 1977–2010.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
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
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
Silverthorne, K. E. & Toole, J. M. 2009 Seasonal kinetic energy variability of near-inertial motions. J. Phys. Oceanogr. 39, 1035–1049.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
Thomas, L. N. 2019 Enhanced radiation of near-inertial energy by frontal vertical circulations. J. Phys. Oceanogr. 49, 2407–2421.CrossRefGoogle Scholar
Thomas, J. & Arun, S. 2020 Near-inertial waves and geostrophic turbulence. Phys. Rev. Fluids 5, 014801.CrossRefGoogle Scholar
Thomas, J., Smith, K. S. & Bühler, O. 2017 Near-inertial wave dispersion by geostrophic flows. J. Fluid Mech. 817, 406–438.CrossRefGoogle Scholar
Thomas, J. & Yamada, R. 2019 Geophysical turbulence dominated by inertia-gravity waves. J. Fluid Mech. 875, 71–100.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
Waite, M. L. 2017 Random forcing of geostrophic motion in rotating stratified turbulence. Phys. Fluid 29, 126602.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
Wortham, C. & Wunsch, C. 2014 A multidimensional spectral description of ocean variability. J. Phys. Oceanogr. 44, 944–966.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
Young, W. R. & Ben Jelloul, M. 1997 Propagation of near-inertial oscillations through a geostrophic flow. J. Mar. Res. 55, 735–766.CrossRefGoogle Scholar
Zeitlin, V., Reznik, G. M. & Jelloul, M. B. 2003 Nonlinear theory of geostrophic adjustment. Part 2. Two-layer and continuously stratified primitive equations. J. Fluid Mech. 491, 207–228.CrossRefGoogle Scholar
Zhai, X., Greatbatch, R. J. & Eden, C. 2007 Spreading of near-inertial energy in a 1/12 degree model of the North Atlantic Ocean. Geophys. Res. Lett. 34, L10609.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