Water Bodies and Stationary Current Conditions at Boundary Surfaces 455 



and 



tan y 



f P2V2 — PiVi 



(X1V.7) 



g P2— Pi 



In each water body there will be a gradient current (geostrophic current). The angles 

 /Si and i3o will determine the slope of the planar isobaric surfaces and that of the 

 physical sea level. 



The slope of the boundary surface is of quite a different order of magnitude. 

 Taking </. = 45° N.; a^ = 28-13; ag = 27-33 (density at 0°C and 35 %o, as well as 

 at 0°C and 34%o) and in addition if the water body 2 is at rest (t'a = 0), while for water 

 body I Vi= 100 cm/sec, then one obtains y = 0°46' 13". The boundary surface is 

 only little inclined to the level surfaces and rises only 13-5 m/km. In the water body at 

 rest the isobaric surfaces are horizontal; in the upper, moving water body they rise 

 very slightly to the right of the current direction because ^i = 0° 0' 2-2", which means 

 a rise of 1 cm in 1 km (Fig. 199; the slopes, in order to make them visible at all, are 

 shown with a considerable vertical exaggeration). The slope of the boundary surface 



i^X 



/ 



-y 



Fig. 199. Stationary current system of two water masses situated side by side (position of 

 the boundary surface, isobaric surfaces and the physical sea surface); GF gradient force; 



CF Coriolis force. 



is about 1000 times greater by magnitude than that of the isobaric surfaces and that 

 of the physical sea level, in the moving water body. Table 131 gives the slopes when 

 Pi = 1-027; P2 = 1-028; v.^ = 0, for different values of ^i at 45 °N. The lighter water 

 mass always glides as a pointed wedge on top of the heavier and superimposes the 

 heavier near the boundary surface as a quite shallow layer. 



Equation (XIV.7) can be simplified if the slope of the isobaric surfaces is neglected 

 by comparison with the much greater slope of the boundary surface. This gives 



tan y = — 



/_ 



S P2 



Pi 



Pi 



(V2 - Vi). 



(XIV. 8) 



