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While Newton explained the tides by describing the tide-generating forces and Daniel Bernoulli gave a description of the static reaction of the waters on Earth to the tidal potential, the dynamic theory of tides, developed by Pierre-Simon Laplace in 1775, [32] describes the ocean's real reaction to tidal forces. [33]
Laplace's theory of ocean tides took into account friction, resonance and natural periods of ocean basins. It predicted the large amphidromic systems in the world's ocean basins and explains the oceanic tides that are actually observed. [32] [33]
Pierre-Simon Laplace formulated a system of partial differential equations relating the ocean's horizontal flow to its surface height, the first major dynamic theory for water tides. The Laplace tidal equations are still in use today.
The basic characteristics of the atmospheric tides are described by the classical tidal theory. [5] By neglecting mechanical forcing and dissipation , the classical tidal theory assumes that atmospheric wave motions can be considered as linear perturbations of an initially motionless zonal mean state that is horizontally stratified and isothermal .
In applied mathematics, the Hough functions are the eigenfunctions of Laplace's tidal equations which govern fluid motion on a rotating sphere. As such, they are relevant in geophysics and meteorology where they form part of the solutions for atmospheric and ocean waves. These functions are named in honour of Sydney Samuel Hough. [1] [2] [3]
The net tide raised on Earth by the Moon is dragged ahead of the Moon by Earth's much faster rotation. Tidal friction is required to drag and maintain the bulge ahead of the Moon, and it dissipates the excess energy of the exchange of rotational and orbital energy between Earth and the Moon as heat.
Of these, Laplace himself was the last, and, perhaps after Newton, the greatest; and the task commenced in the Principia of the former, is completed in the Mécanique Céleste of the latter. In this last named work, the illustrious author has proposed to himself his object, to unite all the theories scattered throughout the various channels of ...
Nevertheless, the predictions of classical tidal theory still did not agree with observations. It was Lindzen, in his 1966 paper, On the theory of the diurnal tide, [24] who showed that the solution set of Hough functions given by Bernhard Haurwitz [25] to Laplace's tidal equation was incomplete: modes with negative equivalent depths had been ...