Triad resonance between gravity and vorticity waves in vertical shear

Weakly nonlinear theory is used to explore the effect of vertical shear on surface gravity waves in three dimensions. An idealized piecewise-linear shear profile motivated by wind-driven profiles and ambient currents in the ocean is used. It is shown that shear may mediate weakly nonlinear resonant triad interactions between gravity and vorticity waves. The triad results in energy exchange between gravity waves of comparable wavelengths propagating in different directions. For realistic ocean shears, shear-mediated energy exchange may occur on timescales of minutes for shorter wavelengths, but slows as the wavelength increases. Hence this triad mechanism may contribute to the larger angular spreading (relative to wind direction) for shorter wind-waves observed in the oceans.