III. THE STORM SURGE EQUATIONS IN THE 

 SHELF COORDINATE SYSTEM 



1. Stretched Shelf Coordinate System . 



Consider the transform-generated coastline and seaward boundary 

 curves as shown in Figure 23. The orthogonal curvilinear mesh asso- 

 ciated with the coordinates (5,n) is designated the shelf coordi- 

 nate system. Although the surge calculations can be performed in 

 the shelf coordinate system (Figure 23b), a problem remains in 

 obtaining the desired spatial resolution with the fewest possible 

 computational points. The computing grid employed (Figure 23c) is 

 the result of a second transformation which preserves the orthogo- 

 nality property but allows independent stretching of £ and of n • 

 The grid resulting from the second transformation is termed the 

 stretched shelf coordinate system (S*,T*). 



The stretched shelf coordinate system is generated by indepen- 

 dently transforming the E, and n axes in the following manner: 



(a) Given the hurricane storm track, the location where 

 the storm crosses the coast and the coastline con- 

 figuration, the values of £ along the coastline 

 are determined which will produce a constant rela- 

 tively fine increment of coastline arc length, S p . 

 In this area of prime interest, line BC in Figure 

 23(a), the constant increment of arc length is 

 equal to AS* . However, regions AB and CD show 

 that for the same AS* as above, there is a rela- 

 tive expansion of the increment of the coastline 

 arc length. The functional relationship between E, 

 and S* is: 



S* = S*(S (O) , (37) 



where the expansion of S_ with respect to S* 

 is specified by an (arbitrary) analytical ex- 

 pression of the form Sp = A + B(S*)C where A , 

 B, and C are constants. 



(b) For the shelf bathymetry along a particular centrally 

 located isoline of E, , the values of n are de- 

 termined which will yield a constant change in the 

 time, AT* , required for a long wave traveling at 

 the local free wave celerity to proceed from seaward 

 boundary to the coast. The long wave travel time, 



T , is calculated by: 



50 



