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In finite water depths, the effects of high winds and linear shear flow (LSF), encompassing both uniform flow and constant vorticity shear flow on freak wave generation are explored. A nonlinear Schrödinger equation, adjusted for high wind and LSF conditions, is derived using potential flow theory and the multiscale method. This equation accounts for the modulational instability (MI) of water waves and the evolution of freak wave amplitudes. MI analysis reveals that for waves to maintain MI, high tail winds (moving in the same direction as the wave) require less vorticity and deeper water, while adverse winds (moving in the opposite direction) necessitate more vorticity and shallower water depths compared to conditions without wind. Uniform up-flows (down-flows), positive (negative) vorticity, and high tail (adverse) winds, which inhibit (promote) wave propagation, increase (decrease) the MI growth rate and amplify (diminish) freak wave heights. It is through this MI that the generation of freak waves is either promoted or inhibited.
Li et al. (Mon,) studied this question.