Basic Principles of the General Oceanic Circulation 585 



(2) a zonal wind circulation (T y= 0); for this the stress on the ocean surface in the 

 interval —s < y < -hs can be given as a Fourier series, a general term of which is 



T^^^ = c + aco^ny + b sin ny with n = j^-; (j =1,2,...) (XVIII.12) 



The solution of (XVIII. 8) which satisfies the boundary conditions is = — rXfS-'^ curl, T 

 whereby 



/ 1 \ r 2 ikx / 



2 -*A^---/V3_ _. ^ J 



1 

 kr 



kx — e-''(^-^) 



1 



west ^ , ' j.(XVIII.13) 



central 



^ , ' 



east 



Here k is the "Coriolis friction" wave-number which has the vale ^(fijA) and is 

 assumed to be constant. The solution is valid as a first approximation when 

 y = (njky <^ 1 and g-''" < 1. When ^ = 0-016 km-^ and r = 6000 km the value of 

 the stream function ip will be accurate within 10%, if y < 0-25, corresponding to a 

 minimum zonal wavelength, lir/n, of about 1500 km. Since for the mean annual 

 stress distribution the shortest wave length of the important north-south variations, 

 the distance between the northern and southern trade winds amount to 4000 km, the 

 approximation leading up to (XVIII. 13) therefore appears to be valid for a study of the 

 general ocean circulation in relationship to the general atmospheric circulation. 



A knowledge of the wind distribution over an ocean thus permits a direct quanti- 

 tative calculation of the current field in the ocean. It was calculated by Munk for the 

 North Pacific, first as an approximation for a rectangular ocean, and later for a tri- 

 angular ocean (Munk and Carrier, 1950), which gives a better representation of 

 actual conditions. 



The solution (XVIII. 13) shows in the first place that the zonal wind system divides 

 the ocean circulation into a number of gyres. The dividing lines between them lie in 

 the latitude of maximum west wind, in the northerly and southerly trade winds and in 

 the doldrums. The latitudinal axis of each gyre may be defined by d^TJdy"^ = 0. The 

 Atlantic Sargasso Sea is associated with the inflection point in the mean wind stress 

 curve between the westerly winds and the north-easterly trades. The inflection points 

 between the doldrums and the northern and southern trades determine the boundary 

 of the equatorial counter current. 



When Xis computed from (XVIII. 13), 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 becomes 



Xwest = \ e-^- cos (^ ^^ - ^) + 1 (XVin.l4) 



representing slightly "underdamped" oscillations with a wavelength given by 



