Flux singularities in multiphase wavetrains and the Kadomtsev‐Petviashvili equation with applications to stratified hydrodynamics

Ratliff, Daniel (2019) Flux singularities in multiphase wavetrains and the Kadomtsev‐Petviashvili equation with applications to stratified hydrodynamics. Studies in Applied Mathematics, 142 (2). pp. 109-138. ISSN 0022-2526

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Official URL: https://doi.org/10.1111/sapm.12242

Abstract

This paper illustrates how the singularity of the wave action flux causes the Kadomtsev-Petviashvili (KP) equation to arise naturally from the modulation of a two-phased wavetrain, causing the dispersion to emerge from the classical Whitham modulation theory. Interestingly, the coefficients of the resulting KP are shown to be related to the associated conservation of wave action for the original wavetrain, and therefore may be obtained prior to the modulation. This provides a universal form for the KP as a dispersive reduction from any Lagrangian with the appropriate wave action flux singularity. The theory is applied to the full water wave problem with two layers of stratification, illustrating how the KP equation arises from the modulation of a uniform flow state and how its coefficients may be extracted from the system.

Item Type: Article
Uncontrolled Keywords: Asymptotic analysis, Lagrangian dynamics, modulation, nonlinear waves, water waves and fluid dynamics
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: John Coen
Date Deposited: 17 Aug 2020 14:52
Last Modified: 18 Aug 2020 09:45
URI: http://nrl.northumbria.ac.uk/id/eprint/44115

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