Linear Theories — Viscous 95 



We may now introduce a transport function xjr, defined by M^ = — d\/rjdy, 

 My=8ijrjdx, and eliminate P by cross-diflFerentiation. We shall assume that 

 fi=dfl8y is a constant, and thus obtain a simple linear equation for i/r: 



/Qi 254 S4\ Q- 



^-"^-f:- *-) 



The boundary conditions are that both ^ and its derivative normal to the 

 boundary shall vanish. If the boundaries (coastlines) are taken as forming 

 a simple rectangle x = 0,r, and y= ±s, and only an east-west wind-stress 

 system is assumed, Ty = 0, then an approximate solution is of the form: 



where 



X=- Be-^^l^^ ^^ cos (^ A;a; + ^ - ^"l + 1 - i {kx - e-^-^' - 1 ) , (32) 

 \ 2 zkr 6/ kr 



where B = i2I^S)-{^3lkr), and k = y{^jA). 



The ^-field which Munk (1950, fig. 2) computed for a rectangular basin 

 of Pacific Ocean dimensions, using mean wind data in the fashion described 

 by Reid (1948 a), is shown in fig. 60. If we consider mean annual zonal 

 winds only, we see that the integrated oceanic wind-driven circulation is 

 divided into closed circulatory systems — or 'gyres', as Munk calls them — 

 bounded at latitudes 0^,, where curlj. t = 0, and with latitudinal axes at 

 latitudes 0^, of extreme values of curl^ t, which of course do not necessarily 

 correspond to latitudes where t = 0. The Sargasso Sea in the Atlantic Ocean 

 is thus situated at the infiection point of the mean wind stress between 

 westerHes and Northern Hemisphere trades. 



The function X{Xi) along the latitude circles ^^ can be interpreted as the 

 total northward transport of the current between x = and x = Xi, whereas 

 the quantity X'{x) is the transport per unit width. Fig. 61 shows these 

 functions drawn to an arbitrary scale. The region from x = to x = 4:/k is 

 supposed to correspond to the Gulf Stream. 



When X and X' are computed it is found that the equations fall naturally 

 into three parts, each of which dominates in a given sector. At the western 

 edge of the ocean x<^r, and 



X^ = - 4 e-<i'2> '^^ cos (y '^^ - ^) + 1 ' (33) 



2 



V3" 



^ = A e-(i/2) kx sm^kx, (34) 



