Nonlinear Waves Passing over Rectangular Obstacles: Multimodal Method and Experimental Validation

Abstract

We report a theoretical and experimental investigation of the propagation of nonlinear waves passing over a submerged rectangular step. A multimodal method allows calculating the first- and second-order reflected and transmitted waves. In particular, at the second order, the propagation of free and bound waves is theoretically presented. A detailed analysis of the convergence of the second-order problem shows that a finite truncation of the series of evanescent bound waves is necessary to obtain a smooth and convergent solution. The computed coefficients of the first and second harmonics are experimentally validated via a complete space-time-resolved measurements of the wave propagation, which permits us to verify the relative amplitude, phase and spatial interference (beating) of the free and bound waves at the second order. This result can be useful in future multimodal models since it not only keeps the accuracy of the model with the inclusion of the first part of the evanescent bound terms (being also the dominants) but also ensures the convergence of the multimodal computation with an error that decreases as a function of the number of modes.

Keywords

• nonlinear waves
• water waves
• free waves
• bound waves
• submerged obstacle