620 The Tropospheric Circulation 



The second part of Rossby's arguments concerns the problem of a straight accel- 

 erated turbulent current. In such a current the horizontal pressure gradient will not be 

 equal to that corresponding to the meari basic current and not balance completely 

 the Coriolis force in stationary equilibrium. This gradient of the stationary current 

 was termed the Coriolis pressure gradient by Rossby and for this the following relations 

 apply 



-^^-p/i; and -^^ ^ + pfu. (XIX.IO) 



A numerical value can always be found for given u and r. The turbulent accelerated 

 motion, however, will be subject to other equations: 



du dp St„„ 



and dv ^ ^P , ^'^vx 



where r^y and Ty^ are the x- and jF-components of the lateral shearing stress. Intro- 

 ducing p = Pc -\- Pr then by means of (XIX.IO) 



and dv dp,. dxy^ 



^dt^~d^'^ '8^' 



The movements which correspond to these equation occur under influence of 

 "residual pressure gradients" Pr as though the earth was not rotating. The continuity 

 equation 



du dv 



ai + a7 = ° *^"''" 



fixes the current field u, v, while (XIX.IO) gives the Coriolis pressure gradient and the 

 corresponding mass field. Since /?(. is usually considerably greater thanpr it is clear that 

 the general pressure distribution is of secondary importance in considering accelerated 

 currents. The mass field which is determined by the mean steady current field gives 

 no information on the cause of the currents. However, according to Rossby /j^ should, 

 dynamically, be more important than p^. 



Against these considerations Defant (1937) and Ekman (1939) have raised doubts 

 affecting more particularly the practical usefulness of the above equations. But 

 nothing can be said generally against the main lines of the basic argument if one 

 remains in agreement with actual conditions. 



For an application of the above equations to Gulf Stream problems Rossby took 

 into account the phenomena that occur when the flow of a medium takes the form of 

 a jet. The theory of free jets (Prandtl, 1926) has been further developed by Tollmien, 

 1926; FoRTHMAN, 1934; Ruden, 1933. For a steady state (du/dt = 0) in a laterally 

 restricted current the first of the equations (XIX. 12) together with the continuity equa- 

 tion (XIX. 13) gives 



pu^ dy = constant, (XIX. 14) 



