Far fields of surface gravity waves generated by a rapidly moving oscillating perturbation source

Abstract

In the paper, the far fields of surface wave perturbations excited by an oscillating localized source rapidly moving in a heavy liquid of infinite depth are studied. It is shown that the excited fields are a sum of two wedge-like waves located insider the corresponding wave wedges. Each of the excited two waves is a complicated wave system of transverse and longitudinal perturbations. The properties of the dispersion curves are studied and the phase pictures describing the structure of wave surface perturbations are calculated. The characteristics of the excited wave fields are studied depending on the basic parameters of the wave generation such as the velocity of motion of the perturbation source and the frequency of its oscillations. Uniform asymptotic solutions are constructed in terms of the Airy function and its derivative, which permits describing the far fields of surface perturbations both outside and inside the corresponding wave wedges.