VARIATIONAL DERIVATION OF THE GREEN–NAGHDI SHALLOW-WATER EQUATIONS
VARIATIONAL DERIVATION OF THE GREEN–NAGHDI SHALLOW-WATER EQUATIONS
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Green-NAGHDI浅水方程的变分推导
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Delia Ionescu
中科院分区：
文献类型：
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作者：
Delia Ionescu
我们考虑具有自由表面和平底的二维无旋水波问题。在浅水区，并且没有对波幅的小假设，我们通过拉格朗日形式主义的变分方法推导出格林-纳格迪方程（1.1）。 (1.1)中的第二个方程是输运方程，自由表面受到流体流动的平流运动。我们证明，在拉格朗日形式主义内，系统的第一个方程（1.1）产生了具有固定端点的路径空间中动作泛函的临界点。
We consider the two-dimensional irrotational water-wave problem with a free surface and a flat bottom. In the shallow-water regime and without smallness assumption on the wave amplitude we derive, by a variational approach in the Lagrangian formalism, the Green–Naghdi equations (1.1). The second equation in (1.1) is a transport equation, the free surface is advected by the fluid flow. We show that the first equation of the system (1.1) yields the critical points of an action functional in the space of paths with fixed endpoints, within the Lagrangian formalism.