Steady-State Solutions of the Wave-Bottom Resonant Interaction

The wave-bottom resonant interaction is investigated by means of analytically solving the fully nonlinear wave equations. It is found that there exist the multiple steady-state resonant waves in the class-I Bragg resonance, whose wave spectrum is time-independent, i. e. without exchange of wave energy between different wave modes. In particular, the resonant wave component may contain less, equal or more wave energy than the primary one in some cases. In addition, there exist the bifurcations of the solutions with respect to the water depth, bottom slope and the angle between the primary and bottom wavenumbers. This work verifies that multiple steady-state resonant waves exist not only in nonlinear wave-wave interaction but also in nonlinear wave-bottom interaction. All of these might deepen our understanding and enrich our knowledge of the resonance of gravity waves.