Mysak 



oj = Wj g_ .) This is not unexpected if we note that the very low minimums of Sg 

 are well to the left of Wj g in Fig. 2. During summer at these stations, however, 

 the behavior in the neighborhood of uJj 14 is distinctly less than barometric for 

 a "true" resonant responsp. (That is, Sj4 at these stations has a minimum when 

 00 - a>j j^ .) Again, this is not too surprising in view of the closeness of the s,^ 

 minimum s to "Jj 14 (Fig. 3). At the west coast, the behavior is distinctly 

 greater than barometric (the observed behavior) only during winter, and in two 

 of the three cases in which this is true the response is also off- resonant to the 

 left, which is also not surprising in view of Fig. 4. While this theory does pre- 

 dict, in many of the cases, the observed behavior when the forcing frequency is 

 in a small neighborhood of an eigenfrequency, the discrepancies which do exist 

 perhaps suggest that bottom friction is not the only amplitude- limiting mecha- 

 nism involved. In fact it can be shown that the terms due to bottom friction (for 

 the values of K given above) are the same order of magnitude as the nonlinear, 

 inertial acceleration terms which have been hitherto neglected. It would thus 

 be of value to determine the theoretical s6a- level response which is damped by 

 both bottom friction and inertial acceleration terms. 



INFLUENCE OF CONTINENTAL SLOPE 



If a finite-slope continental slope region is included in the theory of edge- 

 waves, which are similar in form to continental shelf waves, the wave speed is 

 increased by about 2 percent (11). Since the wavelengths and periods associ- 

 ated with continental shelf waves are much greater, it is quite plausible that a 

 similar geometrical modification would give rise to an even larger increase in 

 the shelf wave speed. In fact it has been suggested (3) that the discrepancy be- 

 tween the observed and theoretical wave speeds may be due to the oversimpli- 

 fied bottom topography used by Robinson (5). Of course the same criticism also 

 applies to the circular model used above. 



To answer this question we assume that between the deep-sea and shelf 

 regions there exists a uniformly sloping continental slope of width t ' with depth 

 d at r = R+ 't and depth D at r = R + f + f. Then it can be shown that to within 

 our order of approximations the eigehfrequencies are given by 



2x7^ - ^oj + qj^^ (mM; j = 1. 2. ...) . (27) 



where q- is a constant of order unity and A' = d-f ' (D- d){. For the case of 

 Australia we take i'-^ = 7.5x10^ cm and C^ = 12.5x10^ cm. For these values of 

 -t' we find that A^ =6x10-^ and a; = 7x10"^. Equation (27) therefore implies 

 that a continental slope region produces a significant shift in the eigenfrequen- 

 cies. For j = 1 the eigenvalue equation implies that qj = -0.9 and -1.1 for the 

 east and west coasts respectively. 



From Eq. (27) the new wave speeds are now readily determined; the results 

 are given in Table 3, along with the theoretical values computed for the previous 

 model and the observed values. From Table 3 we first note that with a continen- 

 tal slope the wave speed at either coast is increased by about 30 percent, which, 

 as conjectured earlier, is much greater than the increase for edgewaves. The 

 theoretical wave speed for the west coast now lies well within the error bounds 



490 



