Unsteady interaction of the surface gravity waves with the nonuniform current

A model of nonstationary interaction between surface and internal waves is developed. Nonlinearity of surface waves is included into analysis by the second order of approximation in wave steepness parameter. Cauchy problem is solved for the initially uniform surface gravity waves on the variable large-scale current induced by internal wave. Various regimes of modulation depend from wave steepness, frequency range and the structure of subsurface current. Surface waves disturbance includes steady wave pattern, connected with the current and moving wave packets, which can form forerunner or tail of the internal wave.