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

Denys Dutykh, Frédéric Dias

Research output: Contribution to journalArticlepeer-review

59 Scopus citations


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 (Joseph and Wang, 2004). Corresponding long wave model equations are derived. To cite this article: D. Dutykh, F. Dias, C. R. Acad. Sci. Paris, Ser. I 345 (2007).

Original languageBritish English
Pages (from-to)113-118
Number of pages6
JournalComptes Rendus Mathematique
Issue number2
StatePublished - 15 Jul 2007


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