Drag coefficient and upstream influence in three-dimensional stratified flow of finite depth

A numerical study of the three-dimensional stratified flow past a vertical square flat plate in a channel of finite depth is described. Particular attention is paid to the anomalous dependence of the drag coefficient C_D on parameter K( = ND/-πU), where N is the Brunt-Väisälä frequency, D is the half depth of the channel and U is the upstream velocity. It is shown that C_D generally increases with K, while it decreases locally at integral values of K. Time development of the upstream columnar disturbance and the corresponding variation of C_D reveals that the periodic variation of C_D with time for K > 1 comes from the successive upstream radiation of the columnar disturbances of the first internal wave mode. Although the propagation speed of the columnar disturbance is consistent with the prediction of linear theory, its time-dependent structure is different from the weakly nonlinear theory as has been shown by laboratory experiments.