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Viscous potential free-surface flows in a fluid layer of finite depth. (English) Zbl 1117.76023
Summary: 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 three-dimensional 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 [D. D. Joseph and J. Wang, J. Fluid Mech. 505, 365–377 (2004; Zbl 1062.76053)].
Reviewer: Reviewer (Berlin)

MSC:
76D27 Other free boundary flows; Hele-Shaw flows
76D05 Navier-Stokes equations for incompressible viscous fluids
76B07 Free-surface potential flows for incompressible inviscid fluids
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