The Tropospheric Circulation 605 



(X.68). In a cross-section through the meridional circulation the water flows towards 

 the equator in the part of the top layer beneath the drift current and rises at the 

 equator. The zonal component of the surface current can be taken as uniform and the 

 relative vorticity/o being zero. If a water layer moves without friction from an initial 

 state ^o> /o' /?o to a new state the vorticity equation gives the relationship 



For water sinking from the surface ^q = 0, and if the thickness is assumed to remain 

 constant during the displacement, and if all the water is assumed to have started from 

 the same initial state, the distribution of the zonal velocity component can be found 

 by integration of 



f+C=fo- (XIX.2) 



For a predominantly zonal current 



dii 1 8ii 



^ 8y R defy 



and for low latitudes the solution can be written in the simpler approximate form 



u-Uo = Roj(<j> - cf^of- (XIX.3) 



If, in the South Equatorial Current, the surface water has a velocity of 0-5 knots with 

 no lateral shear and sinks from latitude (f)Q — 2-1° and flows without friction or 

 changes in thickness to the equator, it will reach the equator as the east undercurrent 

 with a velocity of 2 knots. 



The component of the velocity directed towards the equator in waters moving 

 from latitude 3^ to the equator can also be calculated. The zonal velocity component 

 is given by the equation 



%=fi-gi.,^ (XIX.4) 



where /^.^ is the longitudinal slope of the sea surface at latitude (/>. Its existence is made 

 possible by the presence of the continental barriers. Since 



du dii 



fv - -jj ^fv -V ^ ={f+ i)v =foV 



(XIX.4) can be written in the form 



^ = 7 ix,<i> ~ ^^—r ^x,4>- (XIX. 5) 



/o 2cu9o 



If ^0 = 3°; /o = 7-6 X 10-*' sec-i and i^^ = — 3 x 10-^ (see Montgomery and 

 Palmen (1940) and Jerlov (1953)), the velocity component v towards the equator is 

 —4 cm/sec or 2 nautical miles a day. 



The Equatorial Undercurrent is consistent with the flow towards the equator in 

 the lower part of the top layer close to the equator, if this flow is approximately friction- 

 less so that absolute cyclonic vorticity is conserved. Continental barriers which permit 

 a longitudinal component of the pressure gradient, are essential for any extensive 

 development of the undercurrent. 



