Statistics of weakly nonlinear waves on currents with strong vertical shear

Abstract

We investigate the effect of a vertically sheared current on wave statistics, including the probability of rogue waves, and apply it to a real-world case using measured spectral and shear current data from the mouth of the Columbia River. A theory for weakly nonlinear waves valid to second order in wave steepness is derived and used to analyze statistical properties of surface waves. With the wave spectrum and velocity profile measured in the Columbia River estuary, our theory predicts that the probability of rogue waves is significantly reduced and enhanced during ebb and flood, respectively, supporting the need for shear currents to be accounted for in wave modeling and prediction.