Mysak 



We do not present here the response of 17 to a driving force p which has a 

 continuous frequency distribution of the form shown in Fig. 1; this case will be 

 dealt with in a future paper. 



In view of Eq. (5) we assume a simple harmonic time factor exp (-ic^t) for 

 all the unknown quantities: 



u^(t,4j) >exp(-ia)t). (6) 



Employing Eq. (6), Eqs. (1) and (2) yield, for aj2 ^ i\ 



Bt] f Bt7 \ 



iw 



f2_^2 \^ 3r r Bi/// ' 



Bt] ico Bt] 



(7) 



f ^ + 2^11]. (8) 



Hence Eq. (3) becomes, for h = h(r), 



rhV^T] + h'(r77, _.+ ifaj-^77,^) - r( f ^ - ^2.^ g- 1^ ^ ^^f2_^,2.^^-i^^ exp(ikr cos ^) (9) 



For the circular geometry described in the Introduction, h(r) takes the form 



D, r > R + 't (deep sea region) 



d(r - R)/l, P < r < R+ 't (shelf region) , 



where D is the depth in the deep-sea region, d is the depth at the edge of the 

 shelf, -i is the sheK width, and P is the continental radius. For Australia, 

 D = 5xi05cm, d = 2X10^ cm, ^,3,, ^^^^, -- ^j. = 5xl0^cm, l^^^, ^^^,, -- l^ = 

 7.5 xlO^ cm, and R = 2.05 xlO^ cm. Equation (9) is to be solved separately in 

 the deep-sea and shelf regions, subject to the boundary conditions |t7(R,s^)| < M 

 (a constant) and 17(00, i/;) = . At the edge of the shelf we stipulate that 17 andu^h 

 (radial transport component) be continuous. 



In Eqs. (7), (8), and (9), we assume that ^^ « f ^ Hence in the deep sea 

 region, Eq. (9) reduces to 



(V2- /32)77 = /32cp(j exp(ikr cos i//) , (10) 



where fi^ - f ^/gD. Upon examining the forcing term in Eq. (10), we note that 

 for r - k" * and /^^ « k^, 77 = Oifi^^)^/'^^), which implies that in the deep-sea 

 region the amplitude of 17 is much smaller than that of w . For the case of 

 Australia, the sea-level behavior in the deep-sea region is barometric to within 

 0(10"^) if we set k = ^ x lO"^ cm'^. In the sheK region, Eq. (9) reduces to 



^T7.ff + -^.^ - i7V<^ - eacpg exp(ikR cos 0), < ^ < 1, (11) 



480 



