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Experimental study of parametric subharmonic instability for internal plane waves

Published online by Cambridge University Press:  16 April 2013

Baptiste Bourget ,
Thierry Dauxois ,
Sylvain Joubaud  and
Philippe Odier
Baptiste Bourget
Affiliation:
Laboratoire de Physique de l’École Normale Supérieure de Lyon, Université de Lyon, CNRS, 46 Allée d’Italie, F-69364 Lyon CEDEX 07, France
Thierry Dauxois*
Affiliation:
Laboratoire de Physique de l’École Normale Supérieure de Lyon, Université de Lyon, CNRS, 46 Allée d’Italie, F-69364 Lyon CEDEX 07, France
Sylvain Joubaud
Affiliation:
Laboratoire de Physique de l’École Normale Supérieure de Lyon, Université de Lyon, CNRS, 46 Allée d’Italie, F-69364 Lyon CEDEX 07, France
Philippe Odier
Affiliation:
Laboratoire de Physique de l’École Normale Supérieure de Lyon, Université de Lyon, CNRS, 46 Allée d’Italie, F-69364 Lyon CEDEX 07, France
*
†Email address for correspondence: [email protected]
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Abstract

Internal waves are believed to be of primary importance as they affect ocean mixing and energy transport. Several processes can lead to the breaking of internal waves and they usually involve nonlinear interactions between waves. In this work, we study experimentally the parametric subharmonic instability (PSI), which provides an efficient mechanism to transfer energy from large to smaller scales. It corresponds to the destabilization of a primary plane wave and the spontaneous emission of two secondary waves, of lower frequencies and different wave vectors. Using a time-frequency analysis, we observe the time evolution of the secondary waves, thus measuring the growth rate of the instability. In addition, a Hilbert transform method allows the measurement of the different wave vectors. We compare these measurements with theoretical predictions, and study the dependence of the instability with primary wave frequency and amplitude, revealing a possible effect of the confinement due to the finite size of the beam, on the selection of the unstable mode.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Internal waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 723 , 25 May 2013 , pp. 1 - 20
Copyright
©2013 Cambridge University Press 

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References

Alford, M. H., MacKinnon, J. A., Zhao, Z., Pinkel, R., Klymak, J. & Peacock, T. 2007 Internal waves across the pacific. Geophys. Res. Lett. 34, L24601.Google Scholar
Benielli, D. & Sommeria, J. 1998 Excitation and breaking of internal gravity waves by parametric instability. J. Fluid Mech. 374, 117–144.Google Scholar
Bordes, G., Moisy, F., Dauxois, T. & Cortet, P. P. 2012 Experimental evidence of a triadic resonance of plane inertial waves in a rotating fluid. Phys. Fluids 24 (1), 014105.Google Scholar
Bouruet-Aubertot, P., Sommeria, J. & Staquet, C. 1995 Breaking of standing internal gravity waves through two-dimensional instabilities. J. Fluid Mech. 285, 265–301.Google Scholar
Cairns, J. L. & Williams, G. O. 1976 Internal wave observations from a midwater float, part II. J. Geophys. Res. 81, 1943–1950.CrossRefGoogle Scholar
Carnevale, G. F., Briscolini, M. & Orlandi, P. 2001 Buoyancy- to inertial-range transition in forced stratified turbulence. J. Fluid Mech. 427, 205–239.CrossRefGoogle Scholar
Carter, G & Gregg, M. 2006 Persistent near-diurnal internal waves observed above a site of M2 barotropic-to-baroclinic conversion. J. Phys. Oceanogr. 36, 1136–1146.CrossRefGoogle Scholar
Dalziel, S. B., Hughes, G. O. & Sutherland, B. R. 2000 Whole-field density measurements by ‘synthetic schlieren’. Exp. Fluids 28 (4), 322–335.CrossRefGoogle Scholar
Dauxois, T. & Young, W. R. 1999 Near-critical reflection of internal waves. J. Fluid Mech. 390, 271–295.Google Scholar
Fincham, A & Delerce, G 2000 Advanced optimization of correlation imaging velocimetry algorithms. Exp. Fluids 29 (S), S13–S22.Google Scholar
Flandrin, P. 1999 Time-Frequency/Time-Scale Analysis, Time-Frequency Toolbox for Matlab©. Academic.Google Scholar
Garrett, C. J. R. & Munk, W. H. 1972 Space-time scales of internal waves. Geophys. Fluid Dyn. 3, 225–264.Google Scholar
Gostiaux, L., Didelle, H., Mercier, S. & Dauxois, T. 2007 A novel internal waves generator. Exp. Fluids 42 (1), 123–130.Google Scholar
Hasselmann, K. 1967 A criterion for nonlinear wave stability. J. Fluid Mech. 30 (04), 737–739.CrossRefGoogle Scholar
Hibiya, T., Nagasawa, M. & Niwa, Y. 2002 Nonlinear energy transfer within the oceanic internal wave spectrum at mid and high latitudes. J. Geophys. Res.-Oceans 107 (C11), 3207.Google Scholar
Johnston, T. M. S., Merrifield, M. A. & Holloway, P. E. 2003 Internal tide scattering at the Line Islands Ridge. J. Geophys. Res. 108, 3365.Google Scholar
Joubaud, S., Munroe, J., Odier, P. & Dauxois, T. 2012 Experimental parametric subharmonic instability in stratified fluids. Phys. Fluids 24 (4), 041703.Google Scholar
Koudella, C. R. & Staquet, C. 2006 Instability mechanisms of a two-dimensional progressive internal gravity wave. J. Fluid Mech. 548, 165–196.CrossRefGoogle Scholar
Kunze, E. & Smith, S. G. L. 2004 The role of small-scale topography in turbulent mixing of the global ocean. Oceanography 17 (1), 55–64.Google Scholar
LeBlond, P. H. & Mysak, L. A. 1978 Waves in the Ocean. Elsevier.Google Scholar
MacKinnon, J. A. & Winters, K. B. 2005 Subtropical catastrophe: significant loss of low-mode tidal energy at 28.9 degrees. Geophys. Res. Lett. 32 (15), L15605.Google Scholar
McEwan, A. D. 1971 Degeneration of resonantly-excited standing internal gravity waves. J. Fluid Mech. 50 (03), 431–448.CrossRefGoogle Scholar
McEwan, A. D., Mander, D. W. & Smith, R. K. 1972 Forced resonant second-order interaction between damped internal waves. J. Fluid Mech. 55 (04), 589–608.Google Scholar
McEwan, A. D. & Plumb, R. A. 1977 Off-resonant amplification of finite internal wave packets. Dyn. Atmos. Oceans 2 (1), 83–105.CrossRefGoogle Scholar
McGoldrick, L. F. 1965 Resonant interactions among capillary–gravity waves. J. Fluid Mech. 21 (2), 305–331.Google Scholar
Mercier, M. J., Garnier, N. B. & Dauxois, T. 2008 Reflection and diffraction of internal waves analysed with the Hilbert transform. Phys. Fluids 20 (8), 086601.Google Scholar
Mercier, M. J, Martinand, D., Mathur, M., Gostiaux, L., Peacock, T. & Dauxois, T. 2010 New wave generation. J. Fluid Mech. 657, 308–334.Google Scholar
Munk, W. & Wunsch, C. 1998 Abyssal recipes II: energetics of tidal and wind mixing. Deep-Sea Res. I 45 (12), 1977–2010.CrossRefGoogle Scholar
Munk, W. H. 1966 Abyssal recipes. Deep-Sea Res. Oceanographic Abstracts 13 (4), 707–730.Google Scholar
Peacock, T., Mercier, M., Didelle, H., Viboud, S. & Dauxois, T. 2009 A laboratory study of low-mode internal tide scattering by finite-amplitude topography. Phys. Fluids 21, 121702.Google Scholar
Rainville, L & Pinkel, R. 2006a Baroclinic energy flux at the Hawaiian ridge: observations from the R/P FLIP. J. Phys. Oceanogr. 36 (6), 1104–1122.Google Scholar
Rainville, L. & Pinkel, R. 2006b Propagation of low-mode internal waves through the ocean. J. Phys. Oceanogr. 36, 1220–1236.Google Scholar
Staquet, C. & Sommeria, J. 2002 Internal gravity waves: from instabilities to turbulence. Annu. Rev. Fluid Mech. 34, 559–593.Google Scholar
Susanto, R. D., Mitnik, L. & Zheng, Q. 2005 Ocean internal waves observed in the Lombok Strait. Oceanography 18, 80–87.Google Scholar
Sutherland, B. R. 2010 Internal Gravity Waves. Cambridge University Press.Google Scholar
Thorpe, S. A. 1968 On standing internal gravity waves of finite amplitude. J. Fluid Mech. 32 (03), 489–528.Google Scholar

Bourget et al. supplementary movie

Movie presenting the horizontal (left panel) and vertical (right panel) density gradients for $0< t <193 T_0$ where $T_0 = 2\pi/\omega_0$ is the primary wave period. The wave is propagating from left to the right. Note that the color scale is the same in both panels. The Brunt-V\"ais\"al\"a frequency is $N = 0.91$ rad/s, the primary wave frequency is $\omega_0/N = 0.74$ and the motion amplitude of the plates of the generator is 0.5 cm.

Download Bourget et al. supplementary movie(Video)
Video 8.7 MB