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Energy transfer in resonant and near-resonant internal wave triads for weakly non-uniform stratifications. Part 1. Unbounded domain

Published online by Cambridge University Press:  15 July 2020

Saranraj Gururaj Open the ORCID record for Saranraj Gururaj [Opens in a new window]  and
Anirban Guha Open the ORCID record for Anirban Guha [Opens in a new window]
Saranraj Gururaj
Affiliation:
School of Science and Engineering, University of Dundee, DundeeDD1 4HN, UK
Anirban Guha*
Affiliation:
School of Science and Engineering, University of Dundee, DundeeDD1 4HN, UK
*
†Email address for correspondence: anirbanguha.ubc@gmail.com
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Abstract

In this paper, using multiple-scale analysis, we derive a generalized mathematical model for amplitude evolution, and for calculating the energy exchange in resonant and near-resonant global triads consisting of weakly nonlinear internal gravity wavepackets in weakly non-uniform density stratifications in an unbounded domain in the presence of viscous and rotational effects. Such triad interactions are one of the mechanisms by which high-wavenumber internal waves lead to ocean turbulence and mixing via parametric subharmonic instability. Non-uniform stratification introduces detuning – mismatch in the vertical wavenumber triad condition, which may strongly affect the energy transfer process. We investigate in detail how factors like wavepacket width, group speeds, nonlinear coupling coefficients, detuning and viscosity affect energy transfer in weakly varying stratification. We also investigate the effect of detuning on energy transfer in varying stratification for different daughter wave combinations of a fixed parent wave. We find limitations of the well-known ‘pump-wave approximation’ and derive a non-dimensional number, which can be evaluated from initial conditions, that can predict the maximum energy transferred from the parent wave during the later stages. Two additional non-dimensional numbers, based on various factors affecting energy transfer between near-resonant wavepackets, have also been defined. Moreover, we identify the optimal background stratification in a medium of varying stratification for the parent wave to form a triad with no detuning so that the energy transfer is maximum.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Stratified flows Instability: Parametric instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 899 , 25 September 2020 , A6
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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