A numerical study of stably stratified flows over a two-dimensional hill - Part I. Free-slip condition on the ground

Stably stratified flows over a two-dimensional hill in a channel of finite depth are analyzed numerically by using a newly-developed multi-directional finite-difference method at a Reynolds number Re = 2000. To simplify the phenomena occurring in the flow around the hill, the free-slip condition for the velocity is assumed on the ground, and the nonslip condition is imposed only on the hill surface. Attention is focused on the unsteadiness in the flow around the hill for the cases of K( = NH/πU) > 1 where N and U are the buoyancy frequency and free-stream velocity and H is the domain depth. The flow unsteadiness is discussed, being associated with shedding of the upstream advancing columnar disturbance.