Investigation of Seiche Oscillations in a Free Entrance Bay

Abstract

Seiche oscillations in a free entrance bay are investigated within the framework of the linear theory of long waves in two-dimensional formulation. Analytical solution for a rectangular basin of constant depth for the case when the nodal line of the level is located at the basin entrance is obtained. It is shown that allowance for two-dimensional spatial character is important for transverse seiches: the wave currents depend on two spatial coordinates, and their amplitudes are the functions of the basin width and length. The amplitudes of wave current velocities are the functions of the basin width and length for transversal seiches and are directly proportional to the initial level deviations as well as inversely proportional to square root of the basin depth. It is found that for the longitudinal seiches the wave current velocities are normal to the bay entrance and their maximum values do not depend on its width and length. The longitudinal seiches are characterized by the highest velocities of the wave currents. The features of the seiches in a free entrance basin and in a completely enclosed one are compared, their similarities and differences are determined. The lowest seiche mode in the basin with a free entrance is the Helmholtz mode. It is absent in an enclosed basin and also this mode has no nodal lines within the bay. Wave current for the Helmholtz mode is always directed perpendicularly to the basin entrance and its maximum velocity does not depend on the basin width and length. It is directly proportional to free surface initial deviation and inversely proportional to square root of the basin depth. The lowest current velocities will take place at an open boundary of the basin. The estimates for seiche oscillation periods and wave current velocities approximating the Kruglaya Bay in Sevastopol are obtained.