A numerical study of viscous flows of stably stratified fluids over barriers

Numerical techniques for integrating the Navier-Stokes equations, which were proven useful in the study of homogeneous viscous flows, were extended to handle the flow of a stably stratified viscous fluid over an infinitely long ridge. The flow is considered to be time-dependent, and arbitrary initial conditions were employed. Almost steady-state solutions were computed for Re=10 with Ri=0, 0.25, 2, and 4; and Re=100 with Ri=0.25, where Re and Ri are the Reynolds and Richardson numbers, respectively. An almost periodic solution was found for Re=100 with Ri=2. Two basic velocity profiles were used to demonstrate the dependence of the flow characteristics on the basic flow.