"-£*-*(¥) 



cosh 



[ "2tt(z + d)* | 



27T | Hi L J cos r /x _ tV] (27) 



-,inh[M] l u t ;j 



cosh 

 ? = -a 



sinh 



r -2ir(z + d)" | 



m 



where 



C = the wave celerity 



L = the wavelength 



d = the depth of the undisturbed water 



u = the horizontal velocity of a water particle in the direction 

 of the wave motion 



a = the amplitude of the wave above the undisturbed water level 



T = the wave period 



z = the vertical distance of the particle from the undisturbed 

 water surface 



x = distance measured in the direction of wave motion 



t = time 



£ = the horizontal displacement of the water particle from its 

 undisturbed position 



Tsunamis are shallow-water waves; i.e., the ratio of wavelength to 

 water depth, L/d, is very large. Therefore, equations (26), (27), and 

 (28) can be reduced to more basic small-amplitude, shallow-water equations. 

 Letting d/L -* 0, 



tanh (iH±\ * lid (29) 



39 



