Stability of internal gravity wave modes: from triad resonance to broadband instability
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Author(s)
Akylas, Triantaphyllos R.
Kakoutas, Christos
Date Issued
April 19, 2023
Journal
Journal of Fluid Mechanics
Publisher
Cambridge University Press
Citation
Akylas TR, Kakoutas C. Stability of internal gravity wave modes: from triad resonance to broadband instability. Journal of Fluid Mechanics. 2023;961:A22.
Version
Author's final manuscript
Abstract
A theoretical study is made of the stability of propagating internal gravity wave modes along a horizontal stratified fluid layer bounded by rigid walls. The analysis is based on the Floquet eigenvalue problem for infinitesimal perturbations to a wave mode of small amplitude. The appropriate instability mechanism hinges on how the perturbation spatial scale relative to the basic-state wavelength, controlled by a parameter ๐, compares to the basic-state amplitude parameter, ๐ โช 1. For ๐=๐(1), the onset of instability arises due to perturbations that form resonant triads with the underlying wave mode. For short-scale perturbations such that ๐ โช 1 but ๐ผ = ๐/๐ โซ 1, this triad resonance instability reduces to the familiar parametric subharmonic instability (PSI), where triads comprise fine-scale perturbations with half the basic-wave frequency. However, as ๐ is further decreased holding ๐ fixed, higher-frequency perturbations than these two subharmonics come into play, and when ๐ผ = ๐(1) Floquet modes feature broadband spectrum. This broadening phenomenon is a manifestation of the advection of small-scale perturbations by the basic-wave velocity field. By working with a set of โstreamline coordinatesโ in the frame of the basic wave, this advection can be โfactored outโ. Importantly, when ๐ผ = ๐(1) PSI is replaced by a novel, multi-mode resonance mechanism which has a stabilising effect that provides an inviscid short-scale cut-off to PSI. The theoretical predictions are supported by numerical results from solving the Floquet eigenvalue problem for a mode-1 basic state.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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DOI of Published Version
https://doi.org/10.1017/jfm.2023.265
