Qualitatives Studies of the Tidal Dynamics Equations

Abstract

The spectrum of oscillations observed in the ocean covers a wide frequency range — much wider than the band (from 0.6 x 10⁻⁷ to 3.0 x 10⁻⁵ cycles/s) of forced oscillations generated by the major harmonics of the tidal potential. That is why the general hydrodynamic equations having solutions corresponding to all the components of the spectrum should be modified in much a way as not to contain any extraneous solutions and, at the same time, not to distort the solutions for the limited frequency band of interest to us. For this purpose, to exclude acoustic waves it is assumed that sea water is incompressible, and long (including tidal) waves are selected out of the family of gravitational oscillations, proceeding from the requirement of the smallness of the ratio between the vertical and the horizontal scales of motion. From the continuity equation it then follows that vertical velocities are small in comparison with the horizontal ones.