Two-layer stratified flows over pronounced obstacles at low-to-intermediate Froude numbers

Two-layer stratified flows over abrupt topographic obstacles, simulating relevant situations in oceanographic problems, are investigated numerically and experimentally in a simplified two-dimensional situation. Experimental results and numerical simulations are presented at low-to-intermediate Froude numbers for two different obstacles: one semicylindrical and the other prismatic. In both cases, four different flow regimes downstream of the obstacles are found: (I) subcritical flow, (II) internal hydraulic jump, (III) Kelvin-Helmholtz instability at the interface, and (IV) shedding of billows. The critical values of the Froude number for the transition between different regimes depend strongly on the shape of the obstacle. In regime (III), we show that the characteristics of the lee wave that appears past the obstacle can be explained with a theoretical stability analysis. Almost independence of the vortex shedding frequency with upstream velocity is observed and explained.