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| HAL: hal-00145315, version 3 |
| DOI: 10.1016/j.crma.2007.06.007 |
| Detailed view |  Export this paper |
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| Comptes Rendus Mathematique 345, 2 (2007) 113-118 |
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| Available versions: | v1 (2007-05-09) | v2 (2007-06-10) | v3 (2007-08-02) |
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| Viscous potential free-surface flows in a fluid layer of finite depth |
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| Denys Dutykh 1Frédéric Dias 1 |
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| (2007-07-15) |
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| It is shown how to model weakly dissipative free-surface flows using the classical potential flow approach. The Helmholtz--Leray decomposition is applied to the linearized 3D Navier--Stokes equations. The governing equations are treated using Fourier--Laplace transforms. We show how to express the vortical component of the velocity only in terms of the potential and free-surface elevation. A new predominant nonlocal viscous term is derived in the bottom kinematic boundary condition. The resulting formulation is simple and does not involve any correction procedure as in previous viscous potential flow theories [Joseph2004]. Corresponding long wave model equations are derived. |
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| 1: | Centre de Mathématiques et de Leurs Applications (CMLA) |
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CNRS : UMR8536 – École normale supérieure de Cachan - ENS Cachan |
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| Subject | : | Physics/Mechanics/Mechanics of the fluids Engineering Sciences/Mechanics/Fluids mechanics Physics/Physics/Fluid Dynamics Physics/Physics/Atmospheric and Oceanic Physics Mathematics/Analysis of PDEs Mathematics/Mathematical Physics Physics/Mathematical Physics Nonlinear Sciences/Exactly Solvable and Integrable Systems |
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| potential flow – free-surface flow – viscosity – dissipation – water waves – wave damping |
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| hal-00145315, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00145315 | |
| oai:hal.archives-ouvertes.fr:hal-00145315 | |
| From: Denys Dutykh | |
| Submitted on: Thursday, 2 August 2007 09:35:08 | |
| Updated on: Thursday, 2 August 2007 09:40:34 | |
