Skip to main content
×
×
Home

Stimulated generation: extraction of energy from balanced flow by near-inertial waves

  • Cesar B. Rocha (a1), Gregory L. Wagner (a2) and William R. Young (a1)
Abstract

We study stimulated generation – the transfer of energy from balanced flows to existing internal waves – using an asymptotic model that couples barotropic quasi-geostrophic flow and near-inertial waves with $\text{e}^{\text{i}mz}$ vertical structure, where $m$ is the vertical wavenumber and $z$ is the vertical coordinate. A detailed description of the conservation laws of this vertical-plane-wave model illuminates the mechanism of stimulated generation associated with vertical vorticity and lateral strain. There are two sources of wave potential energy, and corresponding sinks of balanced kinetic energy: the refractive convergence of wave action density into anti-cyclones (and divergence from cyclones); and the enhancement of wave-field gradients by geostrophic straining. We quantify these energy transfers and describe the phenomenology of stimulated generation using numerical solutions of an initially uniform inertial oscillation interacting with mature freely evolving two-dimensional turbulence. In all solutions, stimulated generation co-exists with a transfer of balanced kinetic energy to large scales via vortex merging. Also, geostrophic straining accounts for most of the generation of wave potential energy, representing a sink of 10 %–20 % of the initial balanced kinetic energy. However, refraction is fundamental because it creates the initial eddy-scale lateral gradients in the near-inertial field that are then enhanced by advection. In these quasi-inviscid solutions, wave dispersion is the only mechanism that upsets stimulated generation: with a barotropic balanced flow, lateral straining enhances the wave group velocity, so that waves accelerate and rapidly escape from straining regions. This wave escape prevents wave energy from cascading to dissipative scales.

Copyright
Corresponding author
Email address for correspondence: crocha@ucsd.edu
References
Hide All
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), 140.
Balmforth, N. J. & Young, W. R. 1999 Radiative damping of near-inertial oscillations in the mixed layer. J. Mar. Res. 57 (4), 561584.
Barkan, R., Winters, K. B. & McWilliams, J. C. 2016 Stimulated imbalance and the enhancement of eddy kinetic energy dissipation by internal waves. J. Phys. Oceanogr. 47, 181198.
Bretherton, F. P. & Garrett, C. J. R. 1968 Wavetrains in inhomogeneous moving media. Proc. R. Soc. Lond. A 302, 529554.
Bühler, O. & McIntyre, M. E. 1998 On non-dissipative wave–mean interactions in the atmosphere or oceans. J. Fluid Mech. 354, 301343.
Bühler, O. & McIntyre, M. E. 2005 Wave capture and wave–vortex duality. J. Fluid Mech. 534, 6795.
Cox, S. M. & Matthews, P. C. 2002 Exponential time differencing for stiff systems. J. Comput. Phys. 176 (2), 430455.
Danioux, E., Vanneste, J. & Bühler, O. 2015 On the concentration of near-inertial waves in anticyclones. J. Fluid Mech. 773, R2.
Danioux, E., Vanneste, J., Klein, P. & Sasaki, H. 2012 Spontaneous inertia-gravity-wave generation by surface-intensified turbulence. J. Fluid Mech. 699, 153157.
Fornberg, B. 1977 A numerical study of 2-D turbulence. J. Comput. Phys. 25 (1), 131.
Gertz, A. & Straub, D. N. 2009 Near-inertial oscillations and the damping of midlatitude gyres: a modeling study. J. Phys. Oceanogr. 39 (9), 23382350.
Grimshaw, R. 1975 Nonlinear internal gravity waves in a rotating fluid. J. Fluid Mech. 71 (3), 497512.
Hoskins, B. J. 1975 The geostrophic momentum approximation and the semi-geostrophic equations. J. Atmos. Sci. 32 (2), 233242.
Kassam, A.-K. & Trefethen, L. N. 2005 Fourth-order time-stepping for stiff PDEs. SIAM J. Sci. Comput. 26 (4), 12141233.
Klein, P., Llewellyn Smith, S. G. & Lapeyre, G. 2004 Organization of near-inertial energy by an eddy field. Q. J. R. Meteorol. Soc. 130 (598), 11531166.
Landau, L. D. & Lifshitz, E. M. 2013 Quantum Mechanics: Non-relativistic Theory, vol. 3. Elsevier.
McIntyre, M. E. 2009 Spontaneous imbalance and hybrid vortex–gravity structures. J. Atmos. Sci. 66 (5), 13151326.
McWilliams, J. C. 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 2143.
Meleshko, V. V. & Van Heijst, G. J. F. 1994 On Chaplygin’s investigations of two-dimensional vortex structures in an inviscid fluid. J. Fluid Mech. 272, 157182.
Moehlis, J. & Llewellyn Smith, S. G. 2001 Radiation of mixed layer near-inertial oscillations into the ocean interior. J. Phys. Oceanogr. 31 (6), 15501560.
Muraki, D. J., Snyder, C. & Rotunno, R. 1999 The next-order corrections to quasigeostrophic theory. J. Atmos. Sci. 56 (11), 15471560.
Nagai, T., Tandon, A., Kunze, E. & Mahadevan, A. 2015 Spontaneous generation of near-inertial waves by the Kuroshio Front. J. Phys. Oceanogr. 45 (9), 23812406.
Salmon, R. 2016 Variational treatment of inertia-gravity waves interacting with a quasigeostrophic mean flow. J. Fluid Mech. 809, 502529.
Shakespeare, C. J. & Hogg, A. McC. 2017 Spontaneous surface generation and interior amplification of internal waves in a regional-scale ocean model. J. Phys. Oceanogr. 46 (7), 20632081.
Taylor, S. & Straub, D. N. 2016 Forced near-inertial motion and dissipation of low-frequency kinetic energy in a wind-driven channel flow. J. Phys. Oceanogr. 46 (1), 7993.
Thomas, L. N. 2012 On the effects of frontogenetic strain on symmetric instability and inertia-gravity waves. J. Fluid Mech. 711, 620640.
Vanneste, J. 2013 Balance and spontaneous wave generation in geophysical flows. Annu. Rev. Fluid Mech. 45, 147172.
Wagner, G. L. & Young, W. R. 2015 Available potential vorticity and wave-averaged quasi-geostrophic flow. J. Fluid Mech. 785, 401424.
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, 806837.
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, 143169.
Young, W. R. & Ben Jelloul, M. 1997 Propagation of near-inertial oscillations through a geostrophic flow. J. Mar. Res. 55 (4), 735766.
Young, W. R., Rhines, P. B. & Garrett, C. J. R. 1982 Shear-flow dispersion, internal waves and horizontal mixing in the ocean. J. Phys. Oceanogr. 12 (6), 515527.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed