The derivations above are for the special case in which the waves 

 are of sufficient length relative to depth that the wave velocity is a 

 function only of gravity emd the water depth. In the general case, for 

 small -amplitude waves, 



and the velocity ratio, with gm = gp> is 



(4-15) 





27^^^ 



v.y 



. tanh -T-^ 



yp) 



^ tanh -T— t^ 





P 



Thus, since wavelength is a horizontal dimension, 



27rd \l/2 



tanh 



X, 

 tanh 



V - (l, V/2 X HLZ^ C4-16a) 



and the time ratio is Tj. = (Lh)_/Vj., or 



27rdpY/2 



tanh ^— 



tanh -T — 

 Also, since (eq. 4-12) 



equation (4-16) becomes 



vl/2 

 27rd„DF 

 tanh 2_ 



'' ^ w;" / 2^dvi 



tanh -^r—' 



210 



