We consider the nonlinear interaction problem of surface waves
with a tethered
near-surface buoy. Our objective is to investigate mechanisms for nonlinear
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 the nonlinear wave–buoy
interaction
problem with a robust implicit finite-difference method for the cable–buoy
dynamics.
The numerical scheme accounts for nonlinear wave–wave and wave–body
interactions
up to an arbitrary high order in the wave steepness and is able to treat
extreme motions
of the cable including conditions of negative cable tension. Systematic
simulations
show 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 snapping of
the cable
and the generation of surface waves, which provides a source of strong
(radiation)
damping. As a result of this interaction, the chaotic buoy motion switches
between
two competing modes of snapping response: one with larger average peak
amplitude
and lower characteristic frequency, and 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.