Extreme waves generated by modulational instability on adverse currents

Abstract

Physical experiments focusing on the propagation of gravity waves of finite depth on adverse currents were implemented to examine their effect on the development of the modulational instability and to study the geometric characteristics of extreme waves. A series of wave trains with varying initial steepness, perturbation frequency, and initial perturbed strength were mechanically generated in a wave-current flume. The present results show that opposing currents can speed the growth of the modulational instability, verifying the previous theory qualitatively. A current-modified nonlinear Schrödinger equation can predict the measured sideband growth rates well for wave trains with lower perturbation frequencies, but overestimated those with higher perturbation frequencies. On the other hand, the limiting steepness of extreme waves measured in the presence of opposing currents was smaller than that measured in quiescent water. Additionally, current strength was found to have limited influence on the geometric properties of extreme waves as well as on their limiting steepness.