The Whitham Equation with Surface Tension

Autor:	Dinvay, Evgueni, Moldabayev, Daulet, Dutykh, Denys, Kalisch, Henrik
Rok vydání:	2020
Předmět:	Physics - Fluid Dynamics Mathematics - Analysis of PDEs Mathematics - Numerical Analysis Physics - Atmospheric and Oceanic Physics Physics - Computational Physics
Zdroj:	Nonlinear Dynamics (2017), Vol. 88, pp. 1125-1138
Druh dokumentu:	Working Paper
DOI:	10.1007/s11071-016-3299-7
Popis:	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. Comment: 19 pages, 5 figures, 1 table, 36 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/. arXiv admin note: text overlap with arXiv:1410.8299
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2002.09946 Zobrazit plný text záznamu View this record from Arxiv