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5.1 Tides and Tidal Forcing     continued...

While the rhythmic modulation of sea level and its association with the motion of the sun and the moon must have been noticed since pre-historic times, a better understanding had to wait until Sir Isaac Newton applied his theory of gravitation to explain the underlying physical mechanism. He was able to construct an equilibrium theory of tides, that explained the semi-diurnal nature of tides in most parts of the world. If there were infinite time allowed for adjustment of the ocean to the astronomical forces, it is the equilibrium tides that would be the result. This is however not the case since the tidal forcing varies quite rapidly with time. Resonances in the oceanic response push tides in certain localities to be above the values predicted by the equilibrium theory. While the equilibrium theory predicts two bulges to form, one underneath the moon and the other on the opposite side of the globe, in reality the high water may significantly precede or lag the transit of the moon. These differences are due to the dynamical response of the oceans to tidal forcing. It was Laplace who, a century later, laid the theoretical and mathematical foundations for a modern dynamical theory of ocean tides by considering oceanic tides to be the response of the fluid medium to the astronomical forcing by the sun and moon's gravitational attractions. His equations are similar to equations (83) to (85), but linear and in spherical coordinates. In this approach, the tides result from dynamical balances principally between the tractive forces due to gravitation and the retarding forces due to friction in the water column.