AI Article Synopsis
- - The study focuses on wave breaking in a simple wave transitioning to a calm medium, utilizing the defocusing complex modified KdV equation, where a cubic root singularity is found at the breaking point.
- - This wave breaking is regularized by dispersive effects, resulting in the formation of a dispersive shock wave (DSW), which is described as a modulated periodic wave using Gurevich-Pitaevskii methods and Whitham modulation theory.
- - The research employs the generalized hodograph method to solve for DSW boundaries and accurately determines the phase shift, providing a comprehensive description of the DSW that aligns well with numerical simulations.
Article Abstract
We study the problem of wave breaking for a simple wave propagating to a quiescent medium in the framework of the defocusing complex modified KdV (cmKdV) equation. It is assumed that a cubic root singularity is formed at the wave-breaking point. The dispersive regularization of wave breaking leads to the generation of a dispersive shock wave (DSW). We describe the DSW as a modulated periodic wave in the framework of the Gurevich-Pitaevskii approach based on the Whitham modulation theory. The generalized hodograph method is used to solve the Whitham equations, and the boundaries of the DSW are found. Most importantly, we determine the correct phase shift for the DSW from the generalized phase relationships and the modified Gurevich-Pitaevskii matching conditions, so that a complete description of the DSW is obtained rather than just its envelope. All of our analytical predictions agree well with the numerical simulations.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1063/5.0231741 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Want AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!