The Lagrangian Formulation for Wave Motion with a Shear Current and Surface Tension

IF 1.2 3区 数学 Q2 MATHEMATICS, APPLIED
Conor Curtin, Rossen Ivanov
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引用次数: 0

Abstract

The Lagrangian formulation for the irrotational wave motion is straightforward and follows from a Lagrangian functional which is the difference between the kinetic and the potential energy of the system. In the case of fluid with constant vorticity, which arises for example when a shear current is present, the separation of the energy into kinetic and potential is not at all obvious and neither is the Lagrangian formulation of the problem. Nevertheless, we use the known Hamiltonian formulation of the problem in this case to obtain the Lagrangian density function, and utilising the Euler–Lagrange equations we proceed to derive some model equations for different propagation regimes. While the long-wave regime reproduces the well known KdV equation, the short- and intermediate long wave regimes lead to highly nonlinear and nonlocal evolution equations.

Abstract Image

具有剪切流和表面张力的波动的拉格朗日公式
无旋转波动的拉格朗日公式很简单,它来源于拉格朗日泛函,即系统的动能和势能之差。对于具有恒定涡度的流体,例如存在剪切流时,动能和势能的分离并不明显,问题的拉格朗日公式也不明显。然而,在这种情况下,我们使用已知的问题的哈密顿公式来获得拉格朗日密度函数,并利用欧拉-拉格朗日方程推导出不同传播状态的一些模型方程。虽然长波状态再现了众所周知的KdV方程,但短波和中长波状态导致高度非线性和非局部发展方程。
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来源期刊
CiteScore
2.00
自引率
15.40%
发文量
97
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.
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