Shallow water theory

If the water is deeper than 200 m, the linear long wave equation should be applied. For the region shallower than 200 m, the shallow water theory with a term for bottom friction included should be used. This shallow water theory includes the first order approximation of the amplitude dependent dispersion. Under special conditions, the term for frequency dependent dispersion should be included. If the purpose of the simulation is to determine the runup height, the equations of higher order approximations are not necessary. 

Smith, S.V. (1991) Stoichiometry of C N P fluxes in shallow-water marine ecosystems. In Comparative Analyses of Ecosystems—Patterns, Mechanisms, and Theories (Cole, J.J., Lovett, G., and Findlay, S.G., eds.), pp. 259-286, Springer-Verlag, Berlin. 

As a tsunami nears the shoreUne, its height increases and becomes comparable with the water depth ( shallow water see footnote 27). The shallow water equations including the effect of bottom friction should be applied. The theory still assumes the hydrostatic pressure but it takes into consideration the finiteness of the wave amplitude. The second order phase velocity includes the effect of the elevation of the water surface. This effect causes the higher part of the wave to proceed faster. The frontal slope of the wave thus becomes steeper. If the velocity of the water particles at the front exceeds the local phase velocity, the water projects into the air consequently, a breaking bore is formed. 

In pure water too, the activation barrier for PT is shallow or even absent. PT reactions in water have proven to be very fast and this is referred to as the Grotthuss effect. Theodore von Grotthuss (1785-1822) was a German-Lithuanian baron who contributed to both electrolysis and photochemistry. At this time, neither protons nor the electrodissociation theory was known, of course (it was not even known that the formula for water is H2O). Still, Grotthuss developed a primitive theory that H+ and OH ions are involved in conductivity. This depends on the fact that the water molecules form chains of hydrogen bonds. Protons move stepwise and are almost activationless. Covalent bonds become hydrogen bonds as the charge is passed from... 

The skin friction coefficient at the aquatic-sediment surface. This section provides means for obtaining numerical estimates of the coefficient of skin friction on the water-side of lengthy and flat soil or sediment surfaces positioned beneath a flowing water stream or bottom water marine current. The flowing water situations include surface streams, rivers, estuaries, shallow marine flows, flooded soils, flood plains, and so on. The Cf is then used with the appropriate analogy theory algorithm to obtain a numerical estimate of the water-side MTC. 

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