PHYSICAL PROPERTIES OF SEA WATER 2 1 



one hundred to two hundred times greater than the dynamic viscosity of 

 sea water, indicating that turbulence prevailed although the stability 

 reached values as high as 1500 X 10-^m-i (table 1, p. 23). The eddy 

 diffusivity ranged, however, between 0.05 and 0.06 g/cm/sec, and the 

 ratio \ij \Xe varied from 0.02 to 0.20, but was in all instances smaller than 

 the ratio {dv/dzY/gE, as is required by the theory. 



According to Taylor's theory, turbulence can always be present 

 regardless of how great the stability is, but the type of turbulence must 

 be such that the condition (II, 9) is fulfilled; that is, the rate at which the 

 Reynolds stresses communicate energy to a region must be greater than 

 the rate at which the potential energy of that region increases. This 

 explains why observations in the ocean mostly give smaller values of /Xs 

 than of Me. A velocity gradient of 0.1 m/sec on 100 m is common where 

 the stability is about 10~^m~\ and with these values ^s < 0.1 ju^. Within 

 layers of ver}^ great stability the velocity gradient also is generally great, 

 but the value of Ms becomes even smaller than in the above example. 

 Thus, below the Equatorial Countercurrent in the Atlantic the decrease 

 of velocity in a vertical direction is 6.10~^sec~i and the stability is about 

 5.10~^m~^ With these values, Hs < 7 X 10~^ fie, or, if the eddy viscosity 

 were equal to 10 g/cm/sec, the eddy diffusivity would be less than 0.007; 

 that is, it would approach the value of molecular diffusion. 



No theory has been developed for the state of turbulence which at 

 indifferent equilibrium or at stable stratification characterizes a given 

 pattern of flow, except in the immediate vicinity of a solid boundary 

 surface (p. 119), but it has been demonstrated that the turbulence as 

 expressed b}- the eddy viscosity decreases with increasing stability. 

 Thus, Fjeldstad found that he could obtain satisfactory agreement 

 between observed and computed tidal currents in shallow water by 

 assuming that the eddy viscosity was a function not only of the distance 

 from the bottom but of the stability as well. He introduced the equation 

 Me = /(2;)/(l + aE), where E is the stability and where the factor a was 

 determined empirically. 



Thus the effect of stability on turbulence is twofold. In the first 

 place the turbulence is reduced, leading to smaller values of the eddy 

 viscosity, and, in the second place, the type of the turbulence is altered 

 in such a manner that the accompanying eddy diffusivity becomes smaller 

 than the eddy viscosit3^ The latter change is explained by Jacobsen, 

 who assumed that elements in turbulent motion rapidly give off their 

 momentum to their surroundings, but that other properties are exchanged 

 slowly, and that before equalization has taken place the elements are 

 moved to new surroundings by gravitational forces (p. 19). A possible 

 influence of stability on horizontal turbulence has not been examined, but 

 it has been suggested by Parr that this kind of turbulence increases with 

 increasing stability. 



