惠瑟姆方程近极端解的不稳定性

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics Pub Date : 2023-12-19 DOI:10.1111/sapm.12668

John D. Carter

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引用次数: 0

摘要

惠瑟姆方程是浅水中各种波长的小振幅单向波的演变模型。在实验室实验中，它已被证明能准确模拟波浪的演变。我们计算了惠瑟姆方程的 2π 周期行波解，并对其稳定性进行了数值研究，重点研究了陡度较大的解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Instability of near-extreme solutions to the Whitham equation

The Whitham equation is a model for the evolution of small-amplitude, unidirectional waves of all wavelengths in shallow water. It has been shown to accurately model the evolution of waves in laboratory experiments. We compute $2 π$ -periodic traveling wave solutions of the Whitham equation and numerically study their stability with a focus on solutions with large steepness.

We show that the Hamiltonian oscillates at least twice as a function of wave steepness when the solutions are sufficiently steep. We show that a superharmonic instability is created at each extremum of the Hamiltonian and that between each extremum the stability spectra undergo similar bifurcations. Finally, we compare these results with those from the Euler equations.

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来源期刊

Studies in Applied Mathematics 数学-应用数学

CiteScore

4.30

自引率

3.70%

发文量

审稿时长

>12 weeks

期刊介绍： Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.