Solution of the tidal equations for the M 2 and S 2 tides in the world oceans from a knowledge of the tidal potential alone

Abstract

Laplace’s tidal equations are solved for the M 2 and S 2 tides in the world oceans on the basis of a knowledge of the tidal potential alone. Tidal dissipation was taken to be limited to the coastline, where a fraction of the tidal energy incident on the coast was assumed to be absorbed. The coast was assumed to be either vertical or to have a sloping shelf, the latter model yielding results in better agreement with observations. The main purpose of this investigation was to determine the effects of tidal self-attraction and of tidal loading. A fast iterative method was developed by which these secondary effects could be evaluated. The resulting change is of the order of 10%, and somewhat improves the agreement between the theoretical and observed tides. Tidal dissipation from the M 2 and S 2 tides totals 3.1 x 10 19 erg/s. The total retarding couple exerted by the M 2 and S 2 tides on the Earth comes out at 4.2 x 10 23 dyn cm, yielding a deceleration of the Earth’s rotation from these sources of 1080"/cy 2 . The theoretical tidal values were compared with observations on the northeastern and western coasts of the Pacific, on the western coast of the Atlantic, on New Zealand, and on islands. The theoretical tidal phases are generally within one hour of the observed values; the amplitudes are in reasonable agreement with observations except in zones where there is amplification by the fiord effect. A solution obtained for a ‘smoothed’ coastline showed little change.