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Title: Stability of internal gravity wave modes: from triad resonance to broadband instability
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 $$\mu$$ , compares to the basic-state amplitude parameter, $$\epsilon \ll 1$$ . For $$\mu ={O}(1)$$ , the onset of instability arises due to perturbations that form resonant triads with the underlying wave mode. For short-scale perturbations such that $$\mu \ll 1$$ but $$\alpha =\mu /\epsilon \gg 1$$ , 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 $$\mu$$ is further decreased holding $$\epsilon$$ fixed, higher-frequency perturbations than these two subharmonics come into play, and when $$\alpha ={O}(1)$$ 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 ‘streamline coordinates’ in the frame of the basic wave, this advection can be ‘factored out’. Importantly, when $$\alpha ={O}(1)$$ 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.  more » « less
Award ID(s):
2004589
PAR ID:
10434260
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Journal of Fluid Mechanics
Volume:
961
ISSN:
0022-1120
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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