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Journal Articles Comptes Rendus. Mathématique Year : 2007

Viscous potential free-surface flows in a fluid layer of finite depth

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Abstract

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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Dates and versions

hal-00145315 , version 1 (09-05-2007)
hal-00145315 , version 2 (10-06-2007)
hal-00145315 , version 3 (02-08-2007)

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Denys Dutykh, Frédéric Dias. Viscous potential free-surface flows in a fluid layer of finite depth. Comptes Rendus. Mathématique, 2007, 345 (2), pp.113-118. ⟨10.1016/j.crma.2007.06.007⟩. ⟨hal-00145315v3⟩
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