An approach to the analysis of the interaction of surface waves with depth-varying current fields

An approach is developed for the analysis of the interactions of surface waves with depth-varying current fields. The approach is based on an approximate dispersion relation for wave-current interactions derived from the governing equations of the problem (the inviscid Orr-Sommerfeld equations) coupled with the wave kinematic-wave action formulation of surface wave propagation. The approach is particularly useful in that it focuses directly on the wave parameters of interest (the amplitude, frequency, direction, and wavelength of the wave) and eliminates the requirement to solve the inviscid Orr-Sommerfeld equations to derive these parameters. The validity of the approach is demonstrated by comparisons with exact Orr-Sommerfeld solutions.