Forces and their Relationship to the Structure of the Ocean 



319 



where ii, v, w are the velocity components in the direction of the three co-ordinate 

 axes and A is the Laplace operator 8^l8x^ + 8^l8y^ + 8^l8z^. The quantity v = ixjp 

 is called the kinematic viscosity coefficient and has the dimensions [cm^ sec"^]. For 

 numerical values of ju and v for pure water and for sea-water see Vol. I, Pt, I, p. 104. 

 The actual movement of water masses in the oceans does not correspond to a 

 simple ordered gliding of the individual superimposed layers relative to each other, 

 but is rather a random disorganized movement that takes place in vortices and rolls 

 similar to those which can be seen in a smoke plume. The first type of motion is called 

 layered or laminar and the second turbulent. In turbulent flow there is a transfer of 

 the flow momentum from one layer to another, not by the interchange of molecules 

 as in physical internal friction but by the exchange of large elements of water (eddies) 

 which move rather irregularly back and forth between the diff'erent layers and thus 

 bring about a reduction in the velocity in the direction of the basic current; this is 

 then referred to as virtual internal viscosity or eddy viscosity, which in an analogous 

 way to the molecular viscosity can be characterized by a special eddy viscosity coeffi- 

 cient. It is easily seen that the eddy viscosity, by its nature, will be more eff'ective than 

 the molecular viscosity and is also understood by the numerically much larger viscosity 

 coefficients. However, apart from this, the turbulent coefficient is no longer an in- 

 variable quantity like the molecular viscosity at constant temperature, but depends on 

 the nature and the intensity of the turbulence itself. Further, the components of the 

 frictional force of turbulent viscosity can be expressed in exactly the same way as those 

 in equations (X. 12 and 13) if ju, is replaced by the turbulent viscosity coefficient rj. 

 If this is not constant then, for example, equation (X. 12) is replaced by the expression 



1 a 



p 8z 



('£) 



X.14 



and the same applies for the other expressions in (X. 13). 



To a very large extent ocean currents are movements along quasi-horizontal planes 

 so that the turbulent viscosity for small oceanic spaces is limited to that appearing in 

 connection with layered gUding motion of the water masses. Within the moving water 

 mass turbulence creates a definite vertical velocity profile and tends to maintain it. 

 If there is no viscosity this profile must be linear (see Fig. 135, 1). The velocity of the 



Fig. 135. Main types of vertical velocity distributions: (I) in the case of no friction; (II) in 



the case when friction retards the mean current filament; (III) in the case when friction 



accelerates the mean current filament; (IV) for a constant frictional force. 



filament (a) in the middle of the current is then the mean of the velocities of the ad- 

 jacent upper and lower masses. The accelerating influence of the upper layer will be 

 exactly compensated by the retardation at one of the lower. In case II, where the 



