520 



Currents in a Strait 



Fig. 239. To the theory of ocean currents in sea straits. 



p^= p^-\- gpi(^i — z), however, in the lower layer [z from — {h-^ — i^to — //g] will be 

 P2= Po-\- S(p2 — Pi)(^2 — fh) + ^Pi^i — gp2=- Po is the atmospheric pressure at the 

 sea surface. Putting /Jq = — gPiC then ^ is the displacement of the sea surface produced 

 by an atmospheric pressure p^. The equations of motion in the stationary state, 

 disregarding the Coriolis force and friction on the sides of the channel are then 



-^8-x^^^ 



+ 



7] 8^Ui 



0, 



(XVI.ll) 



Pi ^ /y y\ 



P2 



Pi ^^2 



8^Uo 



+ - — - = 



P2 Sx p dz^ 



If Ci and ^2 are small compared with the depth of the strait then, for a linear slope of 

 the physical sea level, u^ and Wg will be independent of x and the continuity equation 

 will take the simple form 



- /,, - hi 



i^dz^O. (XVI. 12) 



Ml dz + U2 



Jo J -hi 



The volume transport of the upper current must be equal to that of the lower current. 

 The boundary conditions are as follows : 



( 1 ) If there is no wind, dujdz = when z = 0. The effect of a wind along the channel 

 can be taken into account by the assumption 



V 



8ui 



az 



^1 Pa W'-, 



where Pa is the density of the air, k^ is the Taylor constant (equation X.9) and n- is the 

 wind velocity relative to that of the water. Taking diijdz = M for z = allows the 

 effect of the wind to be taken into account. 



(2) At the boundary surface there will be a reversal of the current direction, that is, 

 when z = — hi, then Ui = U2 = (no horizontal motion). 



(3) At the bottom (z = — h^ three different cases of boundary friction can be 



