Evolution of surface waves of finite amplitude in field of inhomogeneous current

The evolution of gravity surface waves of finite amplitude on a localized two-dimensional inhomogeneous current is investigated. A model equation describing the variation of surface wave amplitude has been derived and solved numerically. The time evolution of a two-dimensional pattern of surface waves amplitude, when the inhomogeneous current arises at a certain moment of time is investigated. It is shown, that even a relatively weak inhomogeneous current modifies appreciably the regime of surface waves long-wave instability develop. With increasing time the maximum amplitudes of surface waves at first increase, and then run into constant values, but the surface anomaly structure still continues to grow in complexity. The dependence of surface wave field evolution on the amplitude, wave-length and propagation direction of surface waves is investigated