Mechanics of nonlinear short-wave generation by a moored near-surface buoy

We consider the nonlinear interaction problem of surface waves with a tethe red near-surface buoy. Our objective is to investigate mechanisms for nonli near short surface wave generation in this complete coupled wave-buoy-cable dynamical system. We develop an effective numerical simulation capability coupling an efficient and high-resolution high-order spectral method for th e nonlinear wave-buoy interaction problem with a robust implicit finite-dif ference method for the cable-buoy dynamics. The numerical scheme accounts f or nonlinear wave-wave and wave-body interactions up to an arbitrary high o rder in the wave steepness and is able to treat extreme motions of the cabl e including conditions of negative cable tension. Systematic simulations sh ow that beyond a small threshold value of the incident wave amplitude, the buoy performs chaotic motions, characterized by the snapping of the cable. The root cause of the chaotic response is the interplay between the snappin g of the cable and the generation of surface waves, which provides a source of strong (radiation) damping. As a result of this interaction, the chaoti c buoy motion switches between two competing modes of snapping response: on e with larger average peak amplitude and lower characteristic frequency, an d the other with smaller amplitude and higher frequency. The generated high -harmonic/short surface waves are greatly amplified once the chaotic motion sets in. Analyses of the radiated wave spectra show significant energy at higher frequencies which is orders of magnitude larger than can be expected from nonlinear generation under regular motion.