Eliminating flexural-gravity wave resistance on a moving line load with the double-frequency resonant interaction

We consider a fluid covered by an elastic sheet perturbed by a line load moving at a speed for which the leading wave is double the frequency of the trailing wave. We study resonant interactions among these waves using multiple-scale perturbation analysis and direct numerical simulation with a high-order spectral (HOS) method. We find that simultaneous nonlinear interactions in the leading and trailing wave fields can result in zero wave resistance and a localized, two-component wave packet which is steady in the moving frame. For forcing beneath the elastic sheet rather than above it, we show that the maximum bending stress and wave drag can be nearly double the linear prediction. The double-frequency case we consider is a special case of general triad interactions which can modify the maximum bending stress and wave drag over a wide range of speeds. This work is relevant to safe transportation over sea ice.