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Spontaneous inertia-gravity-wave generation by surface-intensified turbulence

Published online by Cambridge University Press:  24 April 2012

E. Danioux ,
J. Vanneste ,
P. Klein  and
H. Sasaki
E. Danioux
Affiliation:
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, King’s Buildings, Edinburgh EH9 3JZ, UK
J. Vanneste
Affiliation:
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, King’s Buildings, Edinburgh EH9 3JZ, UK
P. Klein
Affiliation:
Laboratoire de Physique des Océans, Ifremer-CNRS-UBO-IRD, 29280 Plouzané, France
H. Sasaki
Affiliation:
Earth Simulator Center, JAMSTEC, 3173-25 Showa-machi, Kanazawa-ku, Yokohama, Kanagawa 236-0001, Japan
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Abstract

The spontaneous generation of inertia-gravity waves (IGWs) by surface-intensified, nearly balanced motion is examined using a high-resolution simulation of the primitive equations in an idealized oceanic configuration. At large scale and mesoscale, the dynamics, which is driven by baroclinic instability near the surface, is balanced and qualitatively well described by the surface quasi-geostrophic model. This however predicts an increase of the Rossby number with decreasing spatial scales and, hence, a breakdown of balance at small scale; the generation of IGWs is a consequence of this breakdown. The wave field is analysed away from the surface, at depths where the associated vertical velocities are of the same order as those associated with the balanced motion. Quasi-geostrophic relations, the omega equation in particular, prove sufficient to separate the IGWs from the balanced contribution to the motion. A spectral analysis indicates that the wave energy is localized around dispersion relation for free IGWs, and decays only slowly as the frequency and horizontal wavenumber increase. The IGW generation is highly intermittent in time and space: localized wavepackets are emitted when thin filaments in the surface density are formed by straining, leading to large vertical vorticity and correspondingly large Rossby numbers. At depth, the IGW field is the result of a number of generation events; away from the generation sites it takes the form of a relatively homogeneous, apparently random wave field. The energy of the IGW field generated spontaneously is estimated and found to be several orders of magnitude smaller than the typical IGW energy in the ocean.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Quasi-geostrophic flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 699 , 25 May 2012 , pp. 153 - 173
Copyright
Copyright © Cambridge University Press 2012

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References

1. Adams, J. 1989 Mudpack: multigrid Fortran software for the efficient solution of linear elliptic partial differential equations. Appl. Maths Comput. 34, 113–146.CrossRefGoogle Scholar
2. Aspden, J. M. & Vanneste, J. 2010 Inertia-gravity-wave generation: a geometric–optic approach. In IUTAM Symposium on Turbulence in the Atmosphere and Oceans (ed. Dritschel, D. ), Springer.Google Scholar
3. Bender, C. M. & Orszag, S. A. 1999 Advanced Mathematical Methods for Scientists and Engineers. Springer.CrossRefGoogle Scholar
4. Blumen, W. 1978 Uniform potential vorticity flow. Part I: theory of wave interactions and two-dimensional turbulence. J. Atmos. Sci. 35, 421–432.Google Scholar
5. Bühler, O. 2009 Waves and Mean Flows. Cambridge University Press.CrossRefGoogle Scholar
6. Capet, X., McWilliams, J. C., Molemaker, M. J. & Shchepetkin, A. F. 2008a Mesoscale to submesoscale transition in the California current system. Part I: flow structure, eddy flux, and observational tests. J. Phys. Oceanogr. 38, 29–43.CrossRefGoogle Scholar
7. Capet, X., McWilliams, J. C., Molemaker, M. J. & Shchepetkin, A. F. 2008b Mesoscale to submesoscale transition in the California current system. Part II: frontal processes. J. Phys. Oceanogr. 38, 44–64.CrossRefGoogle Scholar
8. Capet, X., McWilliams, J. C., Molemaker, M. J. & Shchepetkin, A. F. 2008c Mesoscale to submesoscale transition in the California current system. Part III: energy balance and flux. J. Phys. Oceanogr. 38, 2256–2269.CrossRefGoogle Scholar
9. Danioux, E. & Klein, P. 2008 A resonance mechanism leading to wind-forced motions with a frequency. J. Phys. Oceanogr. 38, 2322–2329.CrossRefGoogle Scholar
10. Danioux, E., Klein, P., Hecht, M., Komori, N., Roullet, G. & Gentil, S. L. 2011 Emergence of wind-driven near-inertial waves in the deep ocean triggered by small-scale eddy vorticity structures. J. Phys. Oceanogr. 41, 1297–1307.CrossRefGoogle Scholar
11. Danioux, E., Klein, P. & Rivière, 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
12. Gill, A. 1982 Atmosphere Ocean Dynamics. Academic.Google Scholar
13. Griffiths, M. & Reeder, M. J. 1996 Stratospheric inertia-gravity waves generated in a numerical model of frontogenesis. I: Model solutions. Q. J. R. Meteorol. Soc. 122, 1153–1174.Google Scholar
14. Held, I., Pierrehumbert, R., Garner, S. & Swanson, K. 1995 Surface quasi-geostrophic dynamics. J. Fluid Mech. 282, 1–20.CrossRefGoogle Scholar
15. Hoskins, B. J. & Bretherton, F. P. 1972 Atmospheric frontogenesis models: mathematical formulation and solutions. J. Atmos. Sci. 29, 11–37.2.0.CO;2>CrossRefGoogle Scholar
16. Hoskins, B., Draghici, I. & Davies, H. 1978 A new look at the -equation. Q. J. R. Meteorol. Soc. 104, 31–38.Google Scholar
17. Juckes, M. 1994 Quasi-geostrophic dynamics of the tropopause. J. Atmos. Sci. 51, 2756–2768.2.0.CO;2>CrossRefGoogle Scholar
18. Karsten, R., Jones, H. & Marshall, J. 2002 The role of eddy transfer in setting the stratification and transport of a circumpolar current. J. Phys. Oceanogr. 32, 39–54.2.0.CO;2>CrossRefGoogle Scholar
19. Klein, P., Hua, B., Lapeyre, G., Capet, X., Gentil, S. L. & Sasaki, H. 2008 Upper ocean turbulence from high-resolution 3D simulations. J. Phys. Oceanogr. 38, 1748–1763.CrossRefGoogle Scholar
20. Kraichnan, R. H. 1971 Inertial-range transfer in two- and three-dimensional turbulence. J. Fluid Mech. 47, 525–535.CrossRefGoogle Scholar
21. Lapeyre, G. & Klein, P. 2006 Dynamics of the upper oceanic layers in terms of surface quasigeostrophy theory. J. Phys. Oceanogr. 36, 165–176.CrossRefGoogle Scholar
22. Large, W., Doney, S. & McWilliams, J. 1994 Oceanic vertical mixing: a review and a model with a non-local boundary layer parameterization. Rev. Geophys. 31, 363–403.CrossRefGoogle Scholar
23. McWilliams, J. C., Molemaker, M. J. & Ólafsdóttir, E. I. 2009 Linear fluctuation growth during frontogenesis. J. Phys. Oceanogr. 39, 3111–3129.CrossRefGoogle Scholar
24. Molemaker, M. J., McWilliams, J. C. & Capet, X. 2010 Balanced and unbalanced routes to dissipation in an equilibrated eady flow. J. Fluid Mech. 654, 35–63.CrossRefGoogle Scholar
25. Muraki, D. J., Snyder, C. & Rotunno, R. 1999 The next order corrections to quasigeostrophic theory. J. Atmos. Sci. 56, 1547–1560.2.0.CO;2>CrossRefGoogle Scholar
26. Nagai, T., Tandon, A. & Rudnick, D. 2006 Two-dimensional ageostrophic secondary circulation at ocean fronts due to vertical mixing and large-scale deformation. J. Geophys. Res. 111, C09038.CrossRefGoogle Scholar
27. Ólafsdóttir, E. I., Olde Daalhuis, A. B. & Vanneste, J. 2008 Inertia-gravity-wave radiation by a sheared vortex. J. Fluid Mech. 596, 169–189.CrossRefGoogle Scholar
28. O’Sullivan, D. & Dunkerton, T. J. 1995 Generation of inertia-gravity waves in a simulated life-cycle of baroclinic instability. J. Atmos. Sci. 52, 3695–3716.2.0.CO;2>CrossRefGoogle Scholar
29. Plougonven, R. & Snyder, C. 2005 Gravity waves excited by jets: propagation versus generation. Geophys. Res. Lett. 32, L18802.CrossRefGoogle Scholar
30. Plougonven, R. & Snyder, C. 2007 Inertia-gravity waves spontaneously excited by jets and fronts. Part I: different baroclinic life cycles. J. Atmos. Sci. 64, 2502–2520.CrossRefGoogle Scholar
31. Reeder, M. J. & Griffiths, M. 1996 Stratospheric inertia-gravity waves generated in a numerical model of frontogenesis. Part II: wave sources, generation mechanisms and momentum fluxes. Q. J. R. Meteorol. Soc. 122, 1175–1195.Google Scholar
32. Rivière, P., Tréguier, A.-M. & Klein, P. 2004 Effects of bottom friction on nonlinear equilibration of an oceanic baroclinic jet. J. Phys. Oceanogr. 34, 416–432.2.0.CO;2>CrossRefGoogle Scholar
33. Shchepetkin, A. & McWilliams, J. 2005 The Regional Oceanic Modeling System (ROMS): a split-explicit, free-surface, topography-following coordinate ocean model. Ocean Model. 9, 347–404.CrossRefGoogle Scholar
34. Snyder, C., Muraki, D., Plougonven, R. & Zhang, F. 2007 Inertia-gravity waves generated within a dipole vortex. J. Atmos. Sci. 64, 4417–4431.CrossRefGoogle Scholar
35. Snyder, C., Skamarock, W. & Rotunno, R. 1993 Frontal dynamics near and following frontal collapse. J. Atmos. Sci. 50, 3194–3211.2.0.CO;2>CrossRefGoogle Scholar
36. Temam, R. & Wirosoetisno, D. 2011 Slow manifolds and invariant sets of the primitive equations. J. Atmos. Sci. 68, 675–682.CrossRefGoogle Scholar
37. Thorpe, S. A. 2005 The Turbulent Ocean. Cambridge University Press.CrossRefGoogle Scholar
38. Vanneste, J. 2008a Asymptotics of a slow manifold. SIAM J. Appl. Dyn. Syst. 7, 1163–1190.CrossRefGoogle Scholar
39. Vanneste, J. 2008b Exponential smallness of inertia-gravity-wave generation at small Rossby number. J. Atmos. Sci. 65, 1622–1637.CrossRefGoogle Scholar
40. Vanneste, J. & Yavneh, I. 2004 Exponentially small inertia-gravity waves and the breakdown of quasi-geostrophic balance. J. Atmos. Sci. 61, 211–223.2.0.CO;2>CrossRefGoogle Scholar
41. Viudez, A. & Dritschel, D. G. 2006 Spontaneous emission of inertia-gravity wave packets by balanced geophysical flows. J. Fluid Mech. 553, 107–117.CrossRefGoogle Scholar
42. Warn, T., Bokhove, O., Shepherd, T. G. & Vallis, G. K. 1995 Rossby number expansions, slaving principles, and balance dynamics. Q. J. R. Meteorol. Soc. 121, 723–739.CrossRefGoogle Scholar
43. Williams, R. T. 1967 Atmospheric frontogenesis: a numerical experiment. J. Atmos. Sci. 24, 627–641.2.0.CO;2>CrossRefGoogle Scholar
44. Zhang, F. 2004 Generation of mesoscale gravity waves in upper-tropospheric jet-front systems. J. Atmos. Sci. 61, 440–457.2.0.CO;2>CrossRefGoogle Scholar