The Tropospheric Circulation 



621 



that is, in a current of this type the momentum {impulse) transport through a current 

 cross-section is constant. Neglecting dp^jcx (which is permissible) and introducing 

 the shearing given by 



'»-'fy 



according to equation (XII. 15), then for a mixing length / = ex (proportional to the 

 distance travelled) a complete solution can be found that fixes the horizontal current 

 profile in the free jet. The very good agreement between theory and experimental 

 results for the current profile in a free jet, is a consequence of the assumption made for 

 the mixing length which is completely valid only for limited dimensions. Whether it is 

 also applicable for the very large dimensions of ocean currents is questionable. 



One consequence of the assumption is also that in a free jet with constant momen- 

 tum transport the mass transport increases downstream, and is in fact proportional to 

 the square root of the distance travelled. Due to the incorporation of surrounding 

 water the current cross-section will increase downstream while the mean velocity will 

 decrease. Since the energy remains the same, the mass transport will increase. Condi- 

 tions are somewhat different if the inflow through the initial cross-section does not 

 start from a point source but has a finite width. The velocity profile in Fig. 291 is 



15 

 \-0-\ 



0-5 



1-0- 

 1-5- 



FiG. 291. Velocity distributions in a jet (Freistrahl, according to Ruden). D, nozzle diameter, 

 all lengths are given as multiples of D. 



based on experimental values for the velocity at different distances from the outlet of 

 a nozzle through which there is a constant inflow. In a free jet there is a core in which 

 the initial velocity and the other properties of the medium remain unchanged for a 

 relatively long distance from the nozzle. The formation of a core region and a surroun- 

 ding one of mixing are characteristic of the phenomena occurring in the ocean under 

 similar conditions. 



These results apply in the absence of rotation. According to Rossby, the principal 

 effect of earth rotation is the formation of a different mass distribution (according to 

 (XIX. 10)) corresponding to the Coriolis pressure force; the velocity profile, however, 

 will not be disturbed further by it. The stationary properties of the current, that is that 

 the stream lines, isobars and contours of the physical sea level coincide, remain more 

 or less unchanged. The deviations from a geostrophic current occurring in the interior 

 of the free jet that are produced by the shearing stress, will be accentuated by the 

 deviations due to inertia. There will thus be an overall dynamic equilibrium. According 



