Continental Shelf Waves 



now arises. For a specified f (^j- or l^) and season (summer or winter), which 

 a-, ^'s are most likely to be excited? (It should be made clear here that although 

 the theoretical shelf wave N, ,^ propagates around the whole continental shelf (of 

 width I ) with a fixed frequency given by Eq. (14), we now wish to apply the theory 

 locally to a small region of the coast in view of the two scales of ^ involved, viz., 

 Z and I . Hence Eq. (14) implies that the eigenfrequencies corresponding to 

 each regi'on will differ.) Figure 1 shows the winter spectrum of the atmospheric 

 pressure at Sydney as a function of frequency along with the eigenfrequencies 

 oij ^ as given by Eq. (14) with f = l-^. For this case it is evident that - j g and 

 Wj g are most apt to be excited since only these eigenfrequencies lie at the peak 

 of the spectrum. For I ^ i^, a similar analysis reveals that - j 5 and xj ^ are 

 most likely to be excited. During summer, the eigenfrequencies most likely to 

 be excited are - j ^^ and - j 15 for I = l^, and w^ g and ojj j^ for I = l^. 



To illustrate the coastal sea-level behavior in the neighborhood of the above 

 specified eigenfrequencies, we use the normalized amplitude 



S^(0,a;;^) - | cp + N ^ ^ „ | ^,^^/cp. 



1 + Ai + 2A„ cos 



mW'+-^j- kR cos ■/> 



(19) 



where 



A^ = eaj rkR)/0.62(m7- 1.44) . 



It is clear that when s^ > l or < l the behavior is greater or less than baro- 

 metric. From Eq. (19) we note that when A = 0(1), the sea-level behavior 

 does depend on /' (as well as on m, w, and l). Hence it is not too surprising 

 that the observed Australian sea level at the east coast is quite different from 

 that at the west coast. In Figs. 2 through 5 the amplitude s^ is plotted as a 

 function of frequency for those east and west coast stations where an anomalous 

 sea-level behavior has been observed during winter and/or summer. These 

 stations are listed in Table 1 along with their observed behavior (<and> repre- 

 sents respectively a less or greater than barometric behavior) and position >//. 

 (We have taken the origin of our coordinate system to lie at Alice Springs, 

 which is the geographic center of Australia.) 



The following were observed from Figs. 2 through 5: 



1. For both I = l^ and l = i^, the amplitude S^ - +co as « ^ a.^^, or 



CO -^ coj^ ^. . This phenomenon arises because both viscosity and nonlinear ef- 

 fects have been neglected. To determine the amplitude when the forcing fre- 

 quency is equal to an eigenfrequency (within the framework of a quasi-steady 

 model), at least one of these effects must be incorporated into equations. In 

 the next section we obtain the solution for the amplitude which is damped by 

 bottom friction. 



2. Behavior at the east coast {l = l^). The behavior at all stations during 

 winter is distinctly less than barometric only when the forcing frequency lies 

 in the neighborhood 5x10'^ < co^^^ - <-o < 2 xlO'^ sec"^ (m = 8,9) (Fig. 2). 



483 



