The Tropospheric Circulation 629 



which, only requires a numerical quadrature; the boundary condition here is (/» = 

 at ;c = 0. 



The application of this theory put forward by Chamey starts with the deter- 

 mination of the two constants in equation (XIX. 26). Taking = at the coast, then i/< 

 is the volume transport of the current. The zero point for y is midway between the 

 Florida Strait and Cape Hatteras ( y = y^), that is, 700 km from both sides. 

 The calculated geostrophic transport in the Florida Strait is approximately 

 30 X 10^ m^ sec~^ and the increase from here to Cape Hatteras is approximately 

 50 X 10« m^ sec-i. 



Hence ^o = 80 x 10^ m^ sec~^ and y has the value 2-55 x 10"^ msec~^ Further- 

 more, in (XIX.27), /o = 0-84 x 10"^ sec-^ and /3 = 1-8 X lO-^^ m-^ sec-^. 



If we postulate that h = when x — 0, y = yo and tp = 0, then substituting these 

 values in equation (XIX. 30) gives 



^„ = /^0„y' =820m (XIX.32) 



which compares well with the observed mean value of 900 m given by Iselin (1936). 



The results of the integrations are shown in Fig. 296. This gives in perspective the 

 calculated position of the boundary surface h by contours of h (full lines) at 100 m 

 intervals and on this surface the stream lines (broken lines) of the volume transport 

 for each 10 million m^ sec~^. On top are given calculated velocity profiles for several 

 cross-sections through the Gulf Stream. Comparison of the position of the internal 

 boundary surface with the observed mean depth of the 10° C isotherm, which gives 

 approximately the lower limit of the Gulf Stream, shows that they are in excellent 

 agreement. The characteristic way in which the current swings away from the coast in 

 the northern part of the region considered can also be seen. This takes place away 

 from any projection of the coast line and is found both in the Gulf Stream and in the 

 Kuroshio. The current profile shows towards higher latitudes an increasing concentra- 

 tion of the current energy towards the left-hand edge (westward intensification). The 

 velocities along the left-hand edge are probably too high in the north but would be 

 reasonable since boundary friction was neglected. 



The theory takes a simple form if a quasi-geostrophic approximation is made, that is, when both 

 M and V are assumed to be geostrophic and when h varies linearly with y, then 



h = ho + H-iy - yo)- 

 With the condition A = //, at x = (at the coast) the solution is 



h = 7i( >•) -(h- h,)e-x'x. (XIX.33) 



The width of the current is given approximately by 



Since at the right-hand edge the lateral velocity at the outer boundary is | i7 1 = (g*lf)H; one obtains 



A = V(mIP). (XIX.34) 



It is apparent that the Gulf Stream is a phenomenon that depends essentially on the variation of the 

 Coriolis parameter with latitude. Observed values of u and j3 give a value for A of about 50 km. 

 V decreases laterally to a quarter at a distance of about 70 km which is in accordance with the down- 

 slope to the right shown in Fig. 294. The geostrophic approximation predicts roughly the character 

 of the current but does not predict all the details. 



