The asymptotic solution of a problem in the theory of waves on the surface of a vortex flow

Abstract

THE PROBLEM of the wave motion of a liquid flowing round a solid cylindrical nucleus with constant vortex velocity is considered. The chosen velocity distribution in the layer of the liquid is close to reality. Asymptotic formulas are obtained which enable the wave distribution pattern on the free surface of the liquid to be clearly represented, and the results are compared with the case of a vortex-free flow. In hydrodynamic problems arising in the study of wave motion in the oceans it is necessary to allow for the curvature of the earth and the occurrence of oceanic currents. In view of its complexity the mathematical problem arising from this has not been developed, not only for the hydrodynamic problem in the general formulation, but also for the simplest case where a liquid layer uniformly covering a solid sphere and subjecty to the simplest circulations is considered. However, this difficulty can be overcome in special problems for particular regions of the ocean. The problem of wave motion on the surface of a liquid layer flowing uniformly round a solid cylinder was solved in [1]. The case of a vortex-free flow was considered. In this paper, using the results obtained in [1], wave propagation on the surface of a liquid layer is investigated for the case of a flow with constant vortex velocity.