Skip to main content Accessibility help
×
Home

Generation and stability of inertia–gravity waves

  • P. Maurer (a1), S. Joubaud (a1) and P. Odier (a1)

Abstract

In the ocean, stratification and rotation allow for the existence of inertia–gravity waves. Instabilities of these waves, such as triadic resonant instability (TRI), may play a key role in the mixing process of the deep ocean. In an experimental set-up, we generate inertia–gravity waves which may become unstable depending on the background rotation and wave frequency. The instability produces secondary waves that match the spatial and temporal resonance conditions of TRI. The effect of rotation is introduced in a pre-existing theory and results in a prediction of the growth rate of TRI in the case of an infinite plane wave. The issue of finite size of the beam is then addressed using a simple model in which we show that the instability is enhanced in a given range of Coriolis parameter. Finally, we compare the experimental threshold of the instability with the model, and find good agreement except at higher rotation rate. At constant primary wave frequency, we analyse the evolution of the secondary wave characteristics with rotation. The appearance of unexpected sub-inertial secondary waves may be related to the discrepancy observed between predicted and experimental thresholds at higher rotation.

Copyright

Corresponding author

References

Hide All
Benielli, D. & Sommeria, J. 1998 Excitation and breaking of internal gravity waves by parametric instability. J. Fluid Mech. 374, 117144.
Bordes, G., Moisy, F., Dauxois, T. & Cortet, P.-P. 2012 Experimental evidence of a triadic resonance of plane intertial waves in a rotating fluid. Phys. Fluids 24, 014105.
Bourget, B., Dauxois, T., Joubaud, S. & Odier, P. 2013 Experimental study of parametric subharmonic instability for internal plane waves. J. Fluid Mech. 723, 120.
Bourget, B., Scolan, H., Dauxois, T., Lebars, M., Odier, P. & Joubaud, S. 2014 Finite-size effects in parametric subharmonic instability. J. Fluid Mech. 759, 739750.
Brouzet, C., Sibgatullin, I. N., Scolan, H., Ermanyuk, E. V. & Dauxois, T. 2016 Internal wave attractors examined using laboratory experiments and 3D simulations. J. Fluid Mech. 793, 109131.
Clark, H. A. & Sutherland, B. R. 2010 Generation, propagation, and breaking of an internal wave beam. Phys. Fluids 22 (7), 076601.
Dalziel, S. B., Hughes, G. O. & Sutherland, B. R. 2000 Whole-field density measurements by synthetic schlieren. Exp. Fluids 28, 322335.
Fincham, A. & Delerce, G. 2000 Advanced optimization of correlation imaging velocimetry algorithms. Exp. Fluids (Suppl.) S13S22.
Flandrin, P. 1999 Time-Frequency/Time-Scale Analysis, Time-Frequency Toolbox for Matlab©. Academic.
Fortuin, J. M. H. 1960 Theory and application of two supplementary methods of constructing density gradient columns. J. Polym. Sci. 44 (144), 505515.
Garrett, C. J. R. & Munk, W. H. 1972 Space-time scales of internal waves. Geophys. Fluid Dyn. 3, 225264.
Gayen, B. & Sarkar, S. 2013 Degradation of an internal wave beam by parametric subharmonic instability in an upper ocean pycnocline. J. Geophys. Res. 118 (9), 46894698.
Gostiaux, L. & Dauxois, T. 2007 Laboratory experiments on the generation of internal tidal beams over steep slopes. Phys. Fluids 19 (2), 028102.
Gostiaux, L., Dauxois, T., Didelle, H., Sommeria, J. & Viboud, S. 2006 Quantitative laboratory observations of internal wave reflection on ascending slopes. Phys. Fluids 18, 056602.
Hasselmann, K. 1967 A criterion for nonlinear wave stability. J. Fluid Mech. 30 (04), 737739.
Hazewinkel, J. & Winters, K. B. 2011 PSI of the internal tide on a 𝛽 plane: flux divergence and near-inertial wave propagation. J. Phys. Oceanogr. 41 (9), 16731682.
Hibiya, T. 2004 Latitudinal dependence of diapycnal diffusivity in the thermocline estimated using a finescale parameterization. Geophys. Res. Lett. 31 (1), L01301.
Karimi, H. H. & Akylas, T. R. 2014 Parametric subharmonic instability of internal waves: locally confined beams versus monochromatic wavetrains. J. Fluid Mech. 757, 381402.
Koudella, C. R. & Staquet, C. 2006 Instability mechanisms of a two-dimensional progressive internal gravity wave. J. Fluid Mech. 548, 165196.
Lien, R. C. & Gregg, M. C. 2001 Observations of turbulence in a tidal beam and across a coastal ridge. J. Geophys. Res. 106 (C3), 4575.
Mackinnon, J. A. 2005 Subtropical catastrophe: significant loss of low-mode tidal energy at 28. 9° . Geophys. Res. Lett. 32 (15), L15605.
Mackinnon, J. A., Alford, M. H., Pinkel, R., Klymak, J. & Zhao, Z. 2013a The latitudinal dependence of shear and mixing in the Pacific transiting the critical latitude for PSI. J. Phys. Oceanogr. 43 (1), 316.
Mackinnon, J. A., Alford, M. H., Sun, O., Pinkel, R., Zhao, Z. & Klymak, J. 2013b Parametric subharmonic instability of the internal tide at 29 °N. J. Phys. Oceanogr. 43 (1), 1728.
McComas, C. H. & Bretherton, F. P. 1977 Resonant interaction of oceanic internal waves. J. Geophys. Res. 82 (9), 13971412.
Mercier, M. J., Garnier, N. B. & Dauxois, T. 2008 Reflection and diffraction of internal waves analyzed with the Hilbert transform. Phys. Fluids 20, 086601.
Mercier, M. J., Martinand, D., Mathur, M., Gostiaux, L., Peacock, T. & Dauxois, T. 2010 New wave generation. J. Fluid Mech. 657, 308334.
Müller, P., Holloway, G., Henyey, F. & Pomphrey, N. 1986 Nonlinear interactions among internal gravity waves. Rev. Geophys. 24 (3), 493.
Oster, G. & Yamamoto, M. 1963 Density gradient techniques. Chem. Rev. 63 (3), 257268.
Simmons, H. L. 2008 Spectral modification and geographic redistribution of the semi-diurnal internal tide. Ocean Model. 21 (3–4), 126138.
Staquet, C. & Sommeria, J. 2002 Internal gravity waves: from instabilities to turbulence. Annu. Rev. Fluid Mech. 34 (1), 559593.
Sun, O. M. & Pinkel, R. 2013 Subharmonic energy transfer from the semidiurnal internal tide to near-diurnal motions over Kaena Ridge, Hawaii. J. Phys. Oceanogr. 43 (4), 766789.
Sutherland, B. R. 2010 Internal Gravity Waves. Cambridge University Press.
Sutherland, B. R. 2013 The wave instability pathway to turbulence. J. Fluid Mech. 724, 14.
Sutherland, B. R., Dalziel, S. B., Hughes, G. O. & Linden, P. F. 1999 Visualization and measurement of internal waves by ‘synthetic schlieren’. Part 1. Vertically oscillating cylinder. J. Fluid Mech. 390, 93126.
Young, W. R., Tsand, Y. K. & Balmforth, N. J. 2008 Near-inertial parametric subharmonic instability. J. Fluid Mech. 607, 2549.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Generation and stability of inertia–gravity waves

  • P. Maurer (a1), S. Joubaud (a1) and P. Odier (a1)

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