Modulation effect of linear shear flow, wind, and dissipation on freak wave generation in finite water depth

Abstract

This paper studies the modulation effect of linear shear flow (LSF), comprising a uniform flow and a shear flow with constant vorticity, combined with wind and dissipation on freak wave generation in water of finite depth. A nonlinear Schrödinger equation (NLSE) modified by LSF, strong wind, and dissipation is derived. This can be reduced to consider the effects of LSF, light wind, and dissipation, and further reduced to include only LSF. The relation between modulational instability (MI) of the NLSE and freak waves represented as a modified Peregrine Breather solution is analyzed. When considering only LSF, the convergence (divergence) effect of uniform up-flow (down-flow) and positive (negative) vorticity increases (decreases) the MI growth rate and promotes (inhibits) freak wave generation. The combined effect of LSF and light wind shows that a light adverse (tail) wind can restrain (amplify) MI and bury (trigger) freak waves. Under the effect of a light tailwind, LSF has the same effect on the MI growth rate and freak wave generation as the case without any wind. The combination of LSF and strong wind enables both adverse and tail winds to amplify MI and trigger freak waves. In the presence of strong wind, LSF has the opposite effect to the case of a light tailwind.