The structure of the bow wave, V-wave, and related wave drag and wake in supercritical ambient flow are investigated in the context of homogeneous hydrostatic flow with a free surface over an isolated two dimensional ($h(x,y)$) obstacle. Based on theoretical analysis and numerical modeling, a steady state regime diagram is constructed for supercritical flow. This study suggests that supercritical flow may have an upstream bow wave shock with state transition from supercritical to subcritical near the centerline, and a V-wave shock in the lee without state transition. However, unlike subcritical flow, neither a flank shock or a normal lee shock is observed, due to the local supercritical environment. Both the bow wave shock and V-wave shock are dissipative and reduce the Bernoulli constant, but the vorticity generation is very weak in comparison with subcritical ambient flow. Thus, in supercritical flow, wakes are weak and eddy shedding is absent.
Formulae for V-wave shape and V-wave drag are given using linear theory. Both formulae compare well with numerical model runs for small obstacles.
These results can be applied to air flow over mountains, river hydraulics and coastal ocean currents with bottom topographies.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics