Mass transport in wave tank

The mass transport induced by a small amplitude progressive wave traveling in a rectangular wave tank is investigated. Attention is focused on the three-dimensional mean flow structure generated by the Stokes boundary layers near the side walls. The mass-transport problem is formulated in terms of vorticity and velocity field. A numerical scheme is developed to solve the coupled transport equation for the vorticity and the Poisson equation for the stream function. It is found that the side-wall boundary layers generate mean downstream vorticities. When the Reynolds number is small, the diffusion process dominates. Therefore, the vorticities generated from the boundary layers are diffused into the entire wave tank. On the other hand, when the Reynolds number is much larger than one, the convection process becomes as important as the diffusion process, the steady vorticities are confined within a small area adjacent to the solid boundaries. When the aspect ratio, width divided by depth, is of the order of magnitude of one, a pair of circulation cells appear on the plane perpendicular to the direction of wave propagation. As the width of the tank increases, more cells appear. The spanwise variations of the mass-transport velocity in the wave propagation direction become more significant when the aspect ratio is larger.