124 



Nonlinear Theories — Inertial 



The arbitrary function F{}Jf*) is determined by matching functions at the 

 outer edge of the boundary layer with observed data. Here we make use of 

 the fact that the higher-order terms in equations (21) and (36) vanish at the 

 outer edge of the boundary layer. 



/ 



■Fiir*), 



D 

 g'D = B{f*). 



(37) 

 (38) 



700 



350 



E 



e OF 



-350 



-700 



50 



100 

 X (km.) 



150 



200 



Fig. 69. Comparison of theoretical results and observational material, 

 according to Charney's (1955) analysis, a, calculated depth D* and mass- 

 transport function ^* of the upper layer; contours of D* (solid lines) are 

 drawn for each 100 m., and streamlines (broken lines) for each 10x10" m.»/sec. 

 h, schematic chart of the observed mean depths of the 10° C. isotherm. The 

 scale of the abscissa is exaggerated so that details of the field will show up 

 better. 



At the outer edge of the boundary layer D is prescribed by observation as 

 a function of y. Since at this place 



u= — 



\dxlf 





we also obtain ^ as a function oft/. Therefore, at the outer edge f/D and g'D 

 are known functions of y, and hence of rjr. In this way Charney (1955) 

 determines F{rp-) and B{}Jr) along the outer edge of the boundary layer, and 

 therefore at every point inside the boundary layer which is coimected with 

 the outer boundary by a transport Hne. 



