Wave blocking and partial transmission in subcritical flows over an obstacle

Abstract

We study and measure the transmission coefficient of counterpropagating shallow-water waves produced by a wave generator and scattered by an obstacle. To precisely compare theoretical predictions and experimental data, we consider $\ensuremath{\sim}25$ frequencies for five subcritical background flows, where the maximum value of the Froude number ranges from 0.5 to 0.75. For each flow, the transmission coefficient displays a sharp transition separating total transmission from wave blocking. Both the width and the central frequency of the transition are in good agreement with their theoretical values. The shape of the obstacle is identical to that used by the Vancouver team in the recent experiment aiming at detecting the analog of stimulated Hawking radiation. Our results are compatible with the observations that have been reported. They complete them by establishing that the contribution of the transmission coefficient cannot be neglected for the lower half of the probed frequency range.