Effects of viscosity and bottom friction on recirculating flows

Abstract

A recent set of coastal experiments (Pattiaratchi et al., 1987), found that the horizontal eddy Reynolds number did not adequately describe the wakes found in the lee of coastal islands. Other flow parameters formulated on bottom friction were found to be much better at describing these wakes. In this paper it is suggested that these findings are caused by the extraction of energy from the flow due to bottom friction, which is the net result of the vertical viscous transfer of momentum through the water column to the seabed. This is in contrast to the horizontal viscous transfer of momentum which results in negligible energy loss to the coast, because of the far larger horizontal scales. It is hypothesized that this difference results in fundamentally different flow regimes and this hypothesis is investigated both analytically and numerically. Conditions for the existence of steady zones of barotropic recirculation under the influence of both horizontal viscosity and bottom friction in the wake behind a bluff body are examined analytically. It is found that such steady recirculation requires the presence of horizontal viscosity and is hindered by the loss of energy due to bottom friction. A numerical model is used to verify and quantify this analytical result for the case of two‐dimensional flow around a circular cylinder, and it is concluded that an appropriate bottom friction number, based on the ratio of scales of the nonlinear and bottom friction terms, may often govern the nature of the recirculation in the lee of coastal islands, instead of the eddy Reynolds number based on horizontal eddy viscosity, as is sometimes assumed.