Currents in a Strait 

 is the biharmonic operator. With the boundary conditions 



at .V = and — I < y < I: M^--- Mq 



at .V = and 



l> y> I: M^ = 0, 



541 



(XVI.27) 



where Mq is the volume transport of the river flow at the mouth (which is assumed to be 

 uniform), the solution of (XVI.26) will be given by 



M„ 



= i^»<|(^ + /)tan-i- 

 Equation (XVI.24) thus gives 



+ / V - / 

 (v - /) tan-1 



X X 



(XV.28) 



/^-^!-/|(>- + /)tan-4-'-(.-/)tan-^-^' 



+ 2An 



y + i 



y-l 



-v' - Cv + 0^ '^'' + (y - 0' 



(XVI.29) 



H 1 1 1 1 1 1 1 1 h 



FiG. 251. Spreading of light river water off the mouth in the ocean for different values of 

 the horizontal exchange, (a) R = 1/500; (b) R = 2/500; (c) R = 4/500; (d) R = 8/500; 

 (e) R = 16/500; (/) R = 32/500. Dashed curves: /= (zero Coriolis parameter, non- 

 rotating system) (according to Takano, 1955). 



