The Whitham Equation with Surface Tension
| Autor: | Henrik Kalisch, Denys Dutykh, Evgueni Dinvay, Daulet Moldabayev |
|---|---|
| Přispěvatelé: | Department of Mathematics, University of Bergen (UiB), Laboratoire de Mathématiques (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI), Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
[PHYS.PHYS.PHYS-FLU-DYN]Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn]
Mathematics::Analysis of PDEs Aerospace Engineering FOS: Physical sciences Ocean Engineering 01 natural sciences 010305 fluids & plasmas Hamiltonian system Surface tension [PHYS.PHYS.PHYS-COMP-PH]Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph] Physics::Fluid Dynamics Mathematics - Analysis of PDEs [NLIN.NLIN-PS]Nonlinear Sciences [physics]/Pattern Formation and Solitons [nlin.PS] Inviscid flow 0103 physical sciences FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Fully dispersive equations [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph] Mathematics - Numerical Analysis 0101 mathematics Electrical and Electronic Engineering Hamiltonian systems Korteweg–de Vries equation Nonlinear Sciences::Pattern Formation and Solitons Physics [PHYS.PHYS.PHYS-AO-PH]Physics [physics]/Physics [physics]/Atmospheric and Oceanic Physics [physics.ao-ph] Whitham equation Applied Mathematics Mechanical Engineering 010102 general mathematics Mathematical analysis Fluid Dynamics (physics.flu-dyn) Numerical Analysis (math.NA) Physics - Fluid Dynamics Euler system Computational Physics (physics.comp-ph) Surface waves 3. Good health Physics - Atmospheric and Oceanic Physics Nonlinear Sciences::Exactly Solvable and Integrable Systems Control and Systems Engineering Capillarity Free surface Atmospheric and Oceanic Physics (physics.ao-ph) Compressibility Physics - Computational Physics Analysis of PDEs (math.AP) |
| Zdroj: | Nonlinear Dynamics Nonlinear Dynamics, Springer Verlag, 2017, 88 (2), pp.1125-1138. ⟨10.1007/s11071-016-3299-7⟩ |
| ISSN: | 0924-090X 1573-269X |
| 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. 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: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink