The propagation of long waves into a semi-infinite channel in a rotating system

Abstract

In this paper the propagation of long waves (tides) into a canal is studied. The canal is assumed to be rotating at constant angular velocity and the depth of the fluid is uniform.The rate of rotation can have a considerable effect on the amplitude of the unattenuated modes in the channel. This is due partly to the modification of the known solution when the rotation is zero, and partly to the fact that even if there is only a single semi-infinite barrier unattenuated waves of a special type (Kelvin waves) may be propagated in the rotating system into what is normally called the ‘shadow’ region behind the barrier (Crease 1956).The purpose of this theoretical investigation is to seek a partial explanation of the behaviour of tides and storm surges in the North Sea. For this reason two models of this region are discussed. In Example I the model is of two parallel semi-infinite barriers in the path of a plane progressive wave, and in Example II there are two parallel barriers, one semi-infinite and the other infinite.The ratio of the observed height of the semi-diurnal M2 tide in the North Sea to the height of the incident tide from the Atlantic lies between the results predicted by the two models and is in closer agreement with the model of Example I.