654 The Tropospheric Circulation 



direction. In addition at this stage only small-scale processes, i.e., processes extending 

 over a period of several days to a week and over a distance of up to 10 km, were 

 considered of interest. The equations of motion are then 



-fv = - I (XIX.60) 



dv 

 8i 



8 / 8v\ r„ 



A is the eddy viscosity, Ty is the northward component of wind stress, T and H is the 

 average thickness of the mixed layer. The corresponding vorticity and divergence 

 equations are 



dt, fwn curl^ T 



dt H H 



(XIX.62) 



/^ - g, (XIX.63) 



where Wf, is the vertical velocity at z = /? (depth of the thermoline). The equation of 

 continuity and a condition for the quasi-isostatic adjustment with g* = g(Ap/p) give 



1 8p 

 w,^-,^. (XIX.64) 



The mutual adjustment between the pressure and the current seems to be completed 

 within a period of one to two days, so that the above equation is reasonable for up to 

 about a week after this first stage of adjustment is over. From the equations (xix.62- 

 64) is obtained 



where k =fl\^{g*H). The boundary condition along the coast {u — 0) will require 



( 



8w\ _A:2 



with the condition w = when x = -co the solution of (XIX. 65) will be 

 k^ 



.^j 



fh Cx ro 



Ty e^a^-f)^! + Ty e-^(^-f) di + e^^ Ty e^^ d^ 

 J — CO J — CO 



(XIX.66) 



It can be shown that 



__ 1 ej; 



^^ ~ y8x 



for values \kx\ > 1 and along the coastline we have 



Wo = y [" Ty e^^ dx . (XIX.67) 



A uniform northerly wind over off-shore water will give rise to a coastal upwelling 



given by 



-« = ^, • (XIX.68) 



