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A numerical study on the energy transfer from surface waves to interfacial waves in a two-layer fluid system

Published online by Cambridge University Press:  12 December 2014

Mitsuhiro Tanaka  and
Kyoichi Wakayama
Mitsuhiro Tanaka*
Affiliation:
Faculty of Engineering, Gifu University, 1-1 Yanagido, Gifu, 501-1193, Japan
Kyoichi Wakayama
Affiliation:
Faculty of Engineering, Gifu University, 1-1 Yanagido, Gifu, 501-1193, Japan
*
†Email address for correspondence: [email protected]
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Abstract

Interaction between surface and interfacial waves with continuous energy spectra in a two-layer density stratified fluid system is investigated numerically. For an initial wave field which consists only of the surface waves all propagating in the same direction, it is confirmed that the spectra $S_{s}(k)$ of the surface waves and $S_{i}(k)$ of the interfacial waves change significantly due to the recently found class 3 triad resonance. When the bulk of the surface wave spectrum $S_{s}(k)$ is initially located well above the critical wavenumber $k_{crit}$, below which the class 3 triad resonance is prohibited, $S_{s}(k)$ downshifts gradually toward the lower wavenumber during the initial stage of evolution. However, this downshift halts when the peak of $S_{s}(k)$ reaches around $k_{crit}$, and after that a steep peak forms in $S_{s}(k)$ around $k_{crit}$. It is confirmed that the timescale of the spectral evolution is of $O(1/{\it\epsilon}^{2})$ (${\it\epsilon}$ is a characteristic non-dimensional wave amplitude) in most of the $k$ space, consistent with the prediction of the wave turbulence theory for a system with a decay-type dispersion relation. However, it is also found that the timescale of the formation and growth of the sharp peak in $S_{s}(k)$ around $k_{crit}$ is of $O(1/{\it\epsilon})$, i.e. the timescale of the deterministic three-wave resonance.

JFM classification

Geophysical and Geological Flows: Internal waves Waves/Free-surface Flows: Surface gravity waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 763 , 25 January 2015 , pp. 202 - 217
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Copyright
© 2014 Cambridge University Press 

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