Hi = angular velocity of earth 



(7.29 X 10"^ radians/second); 



<f) = geographical latitude; 



Tg^, Tgj, = X and y components of surface wind stress; 



"^bx' "^bii ~ ^ ^"^ y components of bottom stress; 



p = mass density of water; 



W^, Wj^ = X and y components of wind speed; 



5 = atmospheric pressure deficit in head of water; 



I, = astronomical tide potential in head of water; 



u, V = X and y components, respectively, of current 

 velocity; 



P = precipitation rate (depth/time) ; 



g = gravitational acceleration; and 



9 = angle of wind measured counterclockwise from 

 the X axis. 



Equations 3-50 and 3-51 are approximate expressions for the equations 

 of motion and Equation 3-52 is the continuity relation for a fluid of 

 constant density. These basic equations provide, for all practical pur- 

 poses, a complete description of the water motions associated with nearly 

 horizontal flows such as the storm surge problem. Since these equations 

 satisfactorily describe the phenomenon involved, a nearly exact solution 

 can only be obtained by using these relations in complete form. 



It is possible to obtain useful approximations by ignoring some terms 

 in the basic equations when they are either equivalent to zero or are 

 negligible, but accurate solutions can be achieved only by retaining the 

 full two-dimensional characteristics of the surge problem. Various sim- 

 plifications (discussed later) can be made by ignoring some of the physi- 

 cal processes. These simplifications may provide a satisfactory estimate, 

 but they must always be considered as only an approximation. 



In the past, simplified methods were used extensively to evaluate 

 storm surge because it was necessary to make all computations manually. 

 Manual solutions of the complete basic equations in two dimensions were 

 prohibitively expensive because of the enormous computational effort. 

 With high speed computers, it is possible to resolve the basic hydro- 

 dynamic relations efficiently and economically. As a result of computers, 

 several workers have recently developed useful mathematical models for 

 computing storm surge. These models have substantially improved accuracy, 

 and provide a means for evaluating the surge in the two horizontal dimen- 

 sions. These more accurate methods are not covered here, but are highly 

 recommended for resolving storm-surge problems where more exactness is 



3-95 



