High-Frequency Instabilities of a Boussinesq–Whitham System: A Perturbative Approach

We analyze the spectral stability of small-amplitude, periodic, traveling-wave solutions of a Boussinesq–Whitham system. These solutions are shown numerically to exhibit high-frequency instabilities when subject to bounded perturbations on the real line. We use a formal perturbation method to estima...

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Bibliographic Details
Published in:Fluids (Basel) 2021-04, Vol.6 (4), p.136
Main Authors: Creedon, Ryan, Deconinck, Bernard, Trichtchenko, Olga
Format: Article
Language:English
Subjects:
Amplitudes
Asymptotic methods
Asymptotic properties
Boussinesq equations
Boussinesq–Whitham systems
Eigenvalues
Fourier transforms
high-frequency instabilities
Numerical analysis
Perturbation methods
spectral stability
Stability analysis
Symmetry
traveling waves
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Summary:We analyze the spectral stability of small-amplitude, periodic, traveling-wave solutions of a Boussinesq–Whitham system. These solutions are shown numerically to exhibit high-frequency instabilities when subject to bounded perturbations on the real line. We use a formal perturbation method to estimate the asymptotic behavior of these instabilities in the small-amplitude regime. We compare these asymptotic results with direct numerical computations.
ISSN:2311-5521
2311-5521
DOI:10.3390/fluids6040136