The differential equations above must be placed into dimensionless forms, 

 as were those for the potential problem discussed previously. For this 

 purpose a characteristic length L^, is introduced to measure horizontal 

 distances, a characteristic depth d^, to measure vertical distances, and 

 a characteristic time T^ to measure times. The selection of these 

 quantities is governed to a considerable extent by the geometry of the 

 environment under consideration. For example, if the problem involved 

 tsunamis in a bay similar to that of Hilo Bay, Hawaii (Palmer, Mulvihill, 

 and Funasaki, 1967), Lc would be the length of the bay, dc the depth 

 at the bay mouth, and Tq the critical period of the bay oscillations. 

 The following dimensionless variables are then introduced: 



""t' ""t'^'i 





u' = — ^ V = — ^, V = f , = ^ 



and 



t 



These variables imply that particle velocities are measured in terms of 

 Cgdc) , vertical distances in terms of dc, horizontal distances in 

 terms of L(,, and times in terms of Tq. Introducing these variables in 

 equations 2-56 and 2-63 to obtain, in the following order. 



and 



where 



^.K'|J=0 (2-69) 



^.K'|^=0 (2-70) 



(gdjl^2j 

 K' = -^. . (2-71) 



The solution of the wave problem for a particular environment would be 

 equations of the form 



77' - r?'(X, Y, T, K', 0) (2-72) 



U' = U'(X, Y, T, K', 0) (2-73) 



and 



V = V'(X, Y, r, K', 0) . (2-74) 



43 



