540 



Currents in a Strait 



This compensation-current phenomenon probably occurs at the mouths of most 

 rivers, especially those carrying large quantities of water but no accurate systematic 

 investigation has been made of these processes. 



The situation is different for processes in the sea remote from the mouth of a river. 

 These are easily handled theoretically (Takano, 1954, 1955) and the stratification in 

 the sea, the vertical and lateral mixing and the turbulence of the current can be taken 

 into account. 



Taking a vertical coast as the j'-axis and at this coast a river mouth where 

 — /<>'</ from which the river water with a constant velocity Uq flows into the 

 open sea at right angles to the coast, then, neglecting inertial terms and any tidal 

 effects present, the equations of motion and the continuity equation will be 



- pfv = 



dp __ 8 / 8u , 



dp 



8y+^^'^'+ 8: 



8z\ ' 8z 

 8 



f(^'S)- 



8pU ^PV ^r. 



8x ^ 8y 



(XVI.22) 



Ah and A^ are the lateral and vertical eddy viscosities and /is the Coriolis parameter 

 which can be assumed constant. 



Assuming that the stress both at the surface (z = — i) and at the bottom (z = d) 

 vanishes and introducing the volume transport {p '^ \) one obtains 



M, 



pu dz and M 



-z 



y= \ pv dz 



(XVI.23) 



and putting P = \ P d^ gives from equation (XVI.22) 



AnVm^^fMy = 



8P 



8^' 



8P 



AnV^My~fM, = ^^, 



8M, ^My^ 



8x "^ 8y 



If the stream function is taken as usual 



84, 



a^ 



then from (XVI. 24) 

 whereby 



M^.= -j-y ^"d ^^ ^ + e:^ ' 



vv -= 0, 



g4 g4 g4 



V * = !- 2 I — 



8x^^ dx^8y^ ^ 8y^ 



(XVI.24) 



(XVI.25) 

 (XVI.26) 



