street^ Chan and Fromm 



with 



r(x,y) = [ (x - x^) + y ] 



and q = 1,0 (the shape factor). This was a linear seamount with a 

 sharp peak where the first derivative of d(x,y) is discontinuous and 

 the higher derivatives are undefined (cf , , Sec. 3.1). Unfortunately, 

 the difficulty of resolution of the island features near the peak was 

 compounded by the fact that to simulate the experimental conditions 

 within our nominal core allotment of 500K bytes we had to use A = 

 0,5 where A = 0,25 would have been preferable. As a consequence, 

 we believe, of the coarse grid the short waves generated by the 

 island wave response are not properly resolved, being of the order 

 of one or two grid divisions. The solution, therefore, while not 

 unbounded, appears unstable. 



On the other hand, Williams and Kartha [ 1966] did not report 

 on the sea- state near the Islands and our results might be physically 

 reasonable. A test using q = 2,0 which gives a dome-like island 

 produced an Af = 4,65 for X = 2Trb/Lo =3.0 which is slightly 

 beyond the range of the experiment. However, this Af value lies, 

 as does our result for q = 1,0, within the uncertainty band of re- 

 sults presented by Williams and Kartha. 



3.4. Stability Analysis 



Initial calculations with APPSIM2 and no iteration, viz, , 

 operating with only a single predictor/corrector step produced some- 

 what ragged results after several tens of time steps. Accordingly, 

 a linear stability analysis was made to examine the amplitude pro- 

 perties of the computational scheme. 



For the stability analysis we set dj: = 1 and defined the 

 constant parameters 



cc = At • Ujj/A 



P = At • Vij /A 



Y = At • T1../A 



R = At/A 



The equations defining the computational scheme were linearized by 

 considering only difference quantities as variables and treating the 

 remaining terms as the constants of Eq, (24). Thus, the prediction 

 Eqs, (16-18) become 



166 



(24) 



