Slip Factor and Slip Velocity on a Permeable Bed

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Abstract

In the present study, a new, simple method for determining the slip velocity (also called the bed velocity) at the solid-fluid interface in the wave boundary layer is proposed. Based on experimental and numerical results, when waves travel over a rigid permeable seabed, a nonzero slip velocity exists at the interface. The defect of a small slip velocity has been found to occur in previous studies and is usually encountered in fluid-porous layer problems. In the wave-rigid permeable seabed problem, the slip effect depends on the properties of the seabed. The slip velocity boundary condition (SVBC) is one specification of the slip conditions and is usually applied to explain the slip phenomenon in a fluid-porous layer problem. However, the traditional SVBC or the slip velocity is only considered in a single flow, and application of SVBC in harmonic motion is still an open problem that necessitates a simple formula for determining the slip velocity in realistic cases.

The Stokes’ second problem and the slip length model (SLM) are applied to derive a new slip velocity and a slip factor in this paper. Both the permeability and the roughness of the seabed are chosen as the slip length. The analytical solution shows that the new slip velocity depends on the wave period and the pressure gradient, and the slip factor is related to the wave Reynolds number, the permeability, and the roughness of the seabed. The resultant slip velocity exhibits good agreement with the experimental results, and the slip factor formula obtained by this present study can be applied to a real seabed.

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