628 



The Tropospheric Circulation 



Taking into account the magnitude of the different terms in the equations (XIX.21) 

 and (XIX.22) these can be written simply as 



1 (dv 



+ g*h + G(<A), 



(XIX.23) 

 (XIX.24) 



where v is given by the second equation of (XIX. 20). The determination of the functions 

 F and G is laborious and requires the use of the outer (seaward) boundary condition. 

 Denoting quantities at this boundary by a bar, it follows from (XIX.23) and (XIX.24), 

 since at the boundary {x = oo) both v and dvjdp are zero, that 



flh^Fi^jj) and g*h = G{^P). 



(XIX.25) 



For X — CO, i/j and h are functions of j^ and also fi is a function of ip, that is, F and G 

 are then also functions of ifj and y. 



Since F and G are in principle to determinate for jc = oo they must also be deter- 

 minable at every point in the interior region connected with the outer boundary by a 

 stream line. It is therefore possible to determine F(4)) and G(ifj) at all interior points. 

 The function ifj is taken as a parabolic function of y which is made plausible by the 

 observations at the eastern edge of the Gulf Stream. 



^ = ^0- y(y - y'of- 



With sufficient accuracy /can be taken as a linear function of >• 



f=fo + Ky-yo) 



which gives finally after some calculation 



and 



which is valid for all values of y and ip. 



The equation (XIX.23) and (XIX.24) then give the final equation 



8i/j f I /dG 

 dh g*h g* \ bijj 



Its solution, subject to the boundary conditions h = h{y) and </< 



/j2 = /;2 + 1/(0 _ 0). 



(XIX.26) 



(XIX.27) 



(XIX.28) 



- F 



0. 



0( >') is 



(XIX.29) 



(XIX.30) 



The velocity v is obtained as a function of ijj and y from the equation (XIX.24) and the 

 values of X corresponding to and y are given by the equation 



dx = 



hv 



(XIX.31) 



