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Excitation of superharmonics by internal modes in non-uniformly stratified fluid

Published online by Cambridge University Press:  16 March 2016

Bruce R. Sutherland
Bruce R. Sutherland*
Affiliation:
Departments of Physics and of Earth and Atmospheric Sciences, University of Alberta, Edmonton, AB, Canada T6G 2E1
*
†Email address for correspondence: bruce.sutherland@ualberta.ca
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Abstract

Theory and numerical simulations show that the nonlinear self-interaction of internal modes in non-uniform stratification results in energy being transferred to superharmonic disturbances forced at twice the horizontal wavenumber and frequency of the parent mode. These disturbances are not in themselves a single mode, but a superposition of modes such that the disturbance amplitude is largest where the change in the background buoyancy frequency with depth is largest. Through weakly nonlinear interactions with the parent mode, the disturbances evolve to develop vertical-scale structures that distort and modulate the parent mode. Because pure resonant wave triads do not exist in non-uniformly stratified fluid, parametric subharmonic instability (PSI) is not evident even though noise is superimposed upon the initial state. The results suggest a new mechanism for energy transfer to dissipative scales (from large to small vertical scale and with frequencies larger and smaller than that of the parent mode) through forcing superharmonic rather than subharmonic disturbances.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Internal waves Instability: Parametric instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 793 , 25 April 2016 , pp. 335 - 352
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Copyright
© 2016 Cambridge University Press 

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Sutherland supplementary movie

Movie of internal mode evolution at a thick interface centred in the domain, corresponding to Figure 2 of the manuscript.

Download Sutherland supplementary movie(Video)
Video 4.2 MB

Sutherland supplementary movie

Movie of internal mode evolution at a thick interface shifted toward the top of the domain, corresponding to snapshot in Figure 6b, with frequency spectrum analysis shown in Figure 8.

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Video 4.4 MB

Sutherland supplementary movie

Movie of internal mode evolution in a model seasonal thermocline, corresponding to Figure 9.

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Video 3.9 MB