Experimental Investigation of Oblique Dispersive Shock Waves in Steady Supercritical Shallow Water Flow

A shallow water experiment is implemented in which a sluice gate controls a supercritical flow that is deflected by a slender wedge. Due to surface wave dispersion, the ensuing steady structure is a spatially extended, oscillatory pattern referred to as an oblique dispersive shock wave (DSW), which is a modulated nonlinear wavetrain limiting to an oblique solitary wave at the trailing edge closest to the wedge. Appropriate variation of water depth, flow speed, and deflection angle results in a bifurcation in the flow pattern. The Bond number B, measuring the effects of surface tension relative to gravity, characterizes the bifurcation. The quantity B = 1/3, corresponding to a fluid depth of approximately 5 mm, is the bifurcation point, where there is a transition between classical and non-classical DSW profiles. They are differentiated by monotonicity in their trailing solitary wave edges and the nonlinear wavetrain that ensues. Surface water wave profiles are measured via the Fourier transform profilometry technique and the reconstructed surface profiles are compared with theoretical predictions for the DSW structure as presented in a companion talk.