Shear-Flow/Free-Surface Interaction In a Density-Stratified Fluid

The two-dimensional interaction of a shear flow with a free surface in a stratified fluid is studied numerically, and the results are compared to the behavior of the same flow in a nonstratified fluid. The shear flow corresponds to the velocity profile in the wake of a partially-submerged object, and the stratification is stable and weak in order to simulate a realistic ocean environment. This study provides physical insight to the problem of the interaction of the shear flow in the wake of components of offshore structures with the ocean surface, as well as the problems of 'traces left on the ocean surface by the viscous wake of ships and artificial upwelling. The behavior of the linear instability of the flow is similar to the nonstratified flow, but the growth rates are smaller. The reduction of the growth rates depends on the degree of stratification, and it is, quantitatively, the same for both branches of the linear instability: Branch I at low wavenumbers, Branch II at high wavenumbers. The nonlinear interaction is studied by a direct simulation of the Euler equations subject to free-surface boundary conditions. For small degrees of stratification, the evolution of the flow is similar to the nonstratified flow, because the stratification terms of the Euler equations remain small. rendering in effect the evolution of the flow decoupled from the evolution of the density field. For larger, degrees of stratification the coupling terms become significant, and the evolution of the flow is affected by the density field, but the effect is weak. In both cases. there is a net increase of the value of the mean density at the free-surface, as the vortices of the shear flow bring dense water up and send light water down.