The Cubic Vortical Whitham Equation
| Autor: | John D. Carter, Henrik Kalisch, Christian Kharif, Malek Abid |
|---|---|
| Přispěvatelé: | Institut de Recherche sur les Phénomènes Hors Equilibre (IRPHE), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2021 |
| Předmět: |
Physics::Fluid Dynamics
Computational Mathematics Applied Mathematics Modeling and Simulation Fluid Dynamics (physics.flu-dyn) General Physics and Astronomy FOS: Physical sciences Physics - Fluid Dynamics [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph] [SHS]Humanities and Social Sciences |
| Zdroj: | Wave Motion Wave Motion, 2022, 110, pp.102883. ⟨10.1016/j.wavemoti.2022.102883⟩ |
| ISSN: | 0165-2125 1878-433X |
| DOI: | 10.48550/arxiv.2110.02072 |
| Popis: | The cubic-vortical Whitham equation is a model for wave motion on a vertically sheared current of constant vorticity in a shallow inviscid fluid. It generalizes the classical Whitham equation by allowing constant vorticity and by adding a cubic nonlinear term. The inclusion of this extra nonlinear term allows the equation to admit periodic, traveling-wave solutions with larger amplitude than the Whitham equation. Increasing vorticity leads to solutions with larger amplitude as well. The stability of these solutions is examined numerically. All moderate- and large-amplitude solutions, regardless of wavelength, are found to be unstable. A formula for a stability cutoff as a function of vorticity and wavelength for small-amplitude solutions is presented. In the case with zero vorticity, small-amplitude solutions are unstable with respect to the modulational instability if kh > 1.252, where k is the wavenumber and h is the mean fluid depth. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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