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- W4366393719 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 $mu$ , 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." @default.
- W4366393719 created "2023-04-21" @default.
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- W4366393719 date "2023-04-19" @default.
- W4366393719 modified "2023-10-17" @default.
- W4366393719 title "Stability of internal gravity wave modes: from triad resonance to broadband instability" @default.
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- W4366393719 doi "https://doi.org/10.1017/jfm.2023.265" @default.
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