Variational Derivation of the Geophysical Green-Naghdi Shallow-water System

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics Pub Date : 2025-09-11 DOI:10.1007/s00021-025-00973-9

Yue Chen, Xingxing Liu

引用次数: 0

Abstract

Under the shallow-water regime and without assuming wave amplitude smallness, we apply the variational approach in the Lagrangian formalism to derive the geophysical Green-Naghdi system. In contrast to the prior derivation in (Fan et al., J. Nonlinear Sci., 32(21), 30 (2022)) that imposed a columnar-flow Ansatz, our method adopts the irrotational-flow assumption (which Fan et al., J. Nonlinear Sci., 32(21), 30 (2022) does not), thereby generating the depth-independent horizontal velocity at leading order.

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地球物理Green-Naghdi浅水系统的变分推导

在浅水状态下，在不假设波幅小的情况下，我们应用拉格朗日形式中的变分方法推导了地球物理Green-Naghdi系统。与[Fan et al.， J.非线性科学]中的先验推导相反。， 32（21), 30(2022)）施加柱状流Ansatz时，我们的方法采用旋转流假设(Fan et al.， J.非线性科学。， 32（21), 30（2022）不），从而在领先顺序产生与深度无关的水平速度。

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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来源期刊

Journal of Mathematical Fluid Mechanics 物理-力学

CiteScore

2.00

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.