General Theory of Ocean Currents in a Homegeneous Sea 



445 



be assumed. If the pressure gradient, due to a suddenly imposed sea surface slope, acts 

 along the positive j-axis there will be an extra term +/(/ (to be added on the right- 

 hand side) in the equation of motion (XIII. 64), where U is the velocity of the steady 

 gradient current (geostrophic current) corresponding to the sea surface slope. This 

 equation must be solved assuming the boundary conditions that for z = : dwjdz = 

 and for z = h\w = and for r = : u- = and for r = oo : iv = U (stationary state) ; 



0-75 



0-50 



0-25 



00 

 0-75 



050 



0-25 



000 

 025 



ooo 



-0-25 

 0-25 



000 

 -025 



4 8 4 



Pendulum hours 



Fig. 192. Upper pair of curves: drift current of an ocean of infinite depth for r = (surface). 

 Lower pair of curves: drift current for hID = 1| and in fact for z = (surface), z//z = 0-3 

 and zjh = 0-6 (north and east components always in units TD/nfj. according to Fr. Defant). 



the velocity components of the steady gradient current are denoted by Ust and Vst- 

 Introducing again u + iv = w, then the equations of motion reduce to the single 

 relation 



For stationary conditions (Bwldt = 0, equation XIII. 30) the solution is given by 

 equation (XIII. 31). Under non-stationary conditions a solution is obtained most easily 

 by assuming 



»*• = n',< - H's<F(0 



with the condition 



/■(od) = for ?= 00. 



This can only be given as a series which, however, converges rapidly. As in the case 

 of developing gradient current, oscillations about the final stationary state with inertia 

 periods and decreasing amplitude are produced in both components. 



