Mysak 

 77 = -^(r,!/') exp[-(iw+ K)t], t > . 



(24) 



Substituting Eq. (24) into Eq. (23), and assuming that oj'^ « f^, K « oj, e « l, 

 and i^V « gd, and that B/3^, B/Bs//, and y are each of order unity, we find that 

 the solution for 77 is the same as that given in the preceding section. However, 

 in view of Eq. (24), the unforced shelf waves now decay with time, in contrast to 

 the inviscid case. But since K << w, the effolding time of these waves is of the 

 order of several years. 



In the forced case, the solution is given by 



7](^,0,t) ::: eacp^ J^ 



i™ Jn,(kR) 



rt: Vroj'" Ji(2 V7oj"i) ^(y-yoj - i^oj K/^) 



xJo(2\%7^) exp[i(nn//-ajt)] (m^) 



(25) 



Hence, to compare the theoretical sea-level behavior at the coast with the ob- 

 served behavior, we consider 



s^C-A.o^;^) 



I + Aj + 2A„ cos 



"1(^ + ^1+ <^r 



kR cos i/* 



(26) 



where 



and 



A = eaj (kR)/0.62 [(ym- 1.44)^ + (1.44 K/co)^] 



1/2 



tan a^ = K/co (7m/1.44- 1), < a^ < tt . 



Equation (26) is the generalization of Eq. (19), so that S^ has the same physical 

 interpretation as S^. But Eq. (26) differs from Eq. (19) in one important way: 

 when CO - ojj ^ (a resonant response), Eq. (26) implies that S^ is finite because 

 of the nonzero term (1.44 K/co)^ in the denominator of A^. Further, for the val- 

 ues of K quoted above, S^ = 0(1) when w = co^ m> ^^ ^^^^ ^^^ hypernonbarometric 

 behavior which occurs in the inviscid model when co - co, is now eliminated. 

 Finally, we note that for k « w the behavior as given by s^ will be essentially 

 the same as that given by S^^ except for w in the small neighborhood \co-co^ J <hco 

 where hco = 0(10-^ to 10"^ sec"^). 



In Table 2 the value of S^ at each station listed in Table 1 is given when 

 CO = CO. CO = oj _ (that is, when co, - co - hco > o), and co - co, ^ . We inter- 

 cept these data as follows: when (S^)^^^^^^^ - l > or < 1 - (S^)^i„i^^„ at a 

 given station and in the neighborhood of a particular ^^i „,, we regard the behav- 

 ior in this case as distinctly greater or less than barometric respectively. With 

 this interpretation we note that at the east coast the behavior is distinctly less 

 than barometric (the observed behavior) in 50 percent of the cases. In partic- 

 ular, at Newcastle, Sydney, and Port Kembla during winter, the behavior in the 

 neighborhood of Wj g is distinctly less than barometric for an "off- resonant" 

 response to the left. (That is, s„ at these stations has a minimum when 



488 



