Simulation of surface gravity waves in the Dyachenko variables on the free boundary of flow with constant vorticity

Abstract

Waves in deep water with constant vorticity in the region bounded by the free surface and the infinitely deep plane bottom are considered. Using the conformal variables and the conformal transform technique, a system of exact integro-differential equations solved relative to the derivatives with respect to time is derived and the equivalent system of equations is obtained in the Dyachenko variables. The efficiency of using the obtained system in the Dyachenko variables for investigating surface wave dynamics on the current of infinite depth with constant vorticity is demonstrated with reference to numerical experiments.