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

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journal contribution
posted on 12.11.2018 by Daniel Ratliff
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 so 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.

Funding

The majority of this work was undertaken whilst in receipt of a fully funded EPSRC PhD studentship from grant no. EP/L505092/1.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Studies in Applied Mathematics

Citation

RATLIFF, D.J., 2018. Flux singularities in multiphase wavetrains and the Kadomtsev-Petviashvili equation with applications to stratified hydrodynamics. Studies in Applied Mathematics, 142 (2), pp.109-138.

Publisher

© Wiley

Version

AM (Accepted Manuscript)

Publisher statement

This is the peer reviewed version of the following article: RATLIFF, D.J., 2018. Flux singularities in multiphase wavetrains and the Kadomtsev-Petviashvili equation with applications to stratified hydrodynamics. Studies in Applied Mathematics, 142 (2), pp.109-138, which has been published in final form at https://doi.org/10.1111/sapm.12242. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.

Acceptance date

19/09/2018

Publication date

2018

ISSN

0022-2526

eISSN

1467-9590

Language

en

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