Tides in the Ocean-Shelf System

As already shown, the natural way of obtaining the necessary information on ocean tides consists in a numerical solution of the corresponding boundary value problem. Though this problem was formulated by Laplace as far back as 1775, all the attempts at solving it, particularly those where a priori information on ocean tides is not used, display such disagreement between each other and the observation data that this makes them hardly suitable for geophysical applications. The situation did not improve very much with the advent of high-capacity computers and efficient numerical methods for solving the equations of tidal dynamics. Today it remains almost the same as 18 years ago, when Munk and Zetler, in their innovative paper [204] outlining the possible pathways of studying open-sea tides wrote: “... mathematicians dealing with tides investigations are still staying ashore, making dubious suppositions on what is going on in the open sea.” One of the possible reasons for the failure of the theoretical approach to describing quantitatively the tides in the open sea is associated with disregard for shelf effects.