Computation of the Motion of Long Water Waves 



III. APPSIM2 



3.1. The Governing Equations and Auxiliary Conditions 



Dimensionless variables are defined below and in Fig. 1 where 

 the physical domains considered are also illustrated. The variables 

 are 



(x,y,Ti,d) = (x ,y ,r\ ,d )do 



t = t*(g/dj 



1/2 



(u,v) = (u ,v )(gd.)' 



where those on the left-hand sides are dimensionless and dQ Is the 

 depth In the deepest part of the simulated wave tank. Here, x and 

 y are fixed, Cartesian coordinates in the horizontal plane; u(x,y,t) 

 and v(x,y,t) are the corresponding mean (vertically- averaged) 

 horizontal fluid velocities; •n(x,y,t) Is the free surface shape, 

 measured from the still or undisturbed water line In the tank, and 

 d(x,y) Is the depth of the still water. 



Q. Shelf (Perspective View) 



PEAK (4) 



b. Submerged Seamounf (Plan View) 



Fig. 1. Definition of symbols and slmiialated wave tanks for APPSIM2 



153 



