论文标题
具有表面张力的Whitham方程
The Whitham Equation with Surface Tension
论文作者
论文摘要
WHITHAM方程作为无定位模型在不可压缩流体表面的非局部模型。使用自由地表水波问题的哈密顿结构和dirichlet-neumann操作员得出了一个非局部模型方程式系统。该系统具有重力和毛细管效应，并且在仅限于单向传播时，该系统将减小到毛细管Whitham方程。从数值上看，在各种缩放机制中，whitham方程比其他模型（如kdv和kawahara equation）更准确地对欧拉系统的自由表面问题进行了更准确的近似。在此处考虑的相对较强的毛细血管的情况下，KDV和Kawahara方程的表现优于whitham方程，而表面张力仅在极性的很长的波浪中。
The viability of the Whitham equation as a nonlocal model for capillary-gravity waves at the surface of an inviscid incompressible fluid is under study. A nonlocal Hamiltonian system of model equations is derived using the Hamiltonian structure of the free surface water wave problem and the Dirichlet-Neumann operator. The system features gravitational and capillary effects, and when restricted to one-way propagation, the system reduces to the capillary Whitham equation. It is shown numerically that in various scaling regimes the Whitham equation gives a more accurate approximation of the free-surface problem for the Euler system than other models like the KdV, and Kawahara equation. In the case of relatively strong capillarity considered here, the KdV and Kawahara equations outperform the Whitham equation with surface tension only for very long waves with negative polarity.
