SECT. 6] TURBULENCE 800 



eddy coefficients of viscosity and diffusion in the vertical direction, Nz and Kz, 

 fall within the range 1 to lO^ cm-/sec while the corresponding coefficients in 

 a horizontal direction, Nn and K},, are in the range 10^ to 10^ cm^/sec. 



The generation of vertical turbulence arises from the association of horizontal 

 shearing stresses and a vertical gradient of velocity. The main generating 

 processes are, therefore : 



( 1 ) The action of wind stress on the surface layer ; 



(2) The effect of bottom friction on currents, particularly tidal currents ; 



(3) The presence of shear in currents due to horizontal pressure gradients. 



Horizontal turbulence may be generated by : 



( 1 ) Horizontal variations in the stress of the wind on the surface ; 



(2) Lateral stresses at coastal boundaries ; 



(3) Horizontal shear in currents, or between adjacent currents. 



The very wide spectrum of horizontal motions existing in the oceans has been 

 described by Stommel (1949). The main energy input is into the large-scale 

 ocean circulations which are due directly to the major wind systems. Next in 

 scale are the large eddies which develop in the main currents and may become 

 detached from them. These in turn give rise to a cascade of eddies of diminishing 

 size. It would appear at first sight that, between the largest and the smallest 

 eddies, there would be a wide spectrum of eddies receiving their energy from 

 those larger than themselves and passing it on to those smaller. Such eddies 

 would be expected to fall in the "inertial sub-range" of the theory of locally 

 isotropic turbulence, so that the results of this theory, such as the L^l^ law of 

 eddy viscosity, could be applied to them. The situation is complicated, how- 

 ever, as Stommel pointed out, by the possibility that energy may be injected 

 directly into eddies of almost any intermediate scale, e.g. by local storms or 

 squalls or by tidal currents. These eddies would not then be in the energy 

 equilibrium postulated in the theoretical spectrum and could not be strictly 

 isotropic. 



In dealing with horizontal motions, the choice of a suitable scale of averaging 

 when separating them into mean motion and turbulence is highly significant. 

 Eddies of, say, 50 km in diameter might be treated dynamically as individual 

 entities, if observations spaced sufficiently closely in space and time were 

 available ; or they might be treated statistically as turbulence aff"ecting the 

 main circulation. 



In addition to the paper by Stommel (1949), the application of general ideas 

 on turbulence to oceanographic problems has been discussed by von Karman 

 (1948) and Defant (1954). The mixing of sea-water by turbulence was con- 

 sidered by Proudman (1948) on the basis of Taylor's theory of diffusion by 

 continuous movements (page 804). He showed that, except in special cases, the 

 distribution of a property, such as salinity, could not be expressed in terms of 

 coefficients Kx, Ky and Kz as usually defined. Eckart (1948) distinguished 

 between "stirring" and "mixing" processes, designating by "stirring" the dis- 

 tortion of elements of fluid by a shearing current. The large gradients in the 



