SECT. 6] TURBULENCE 817 



depth, while that generated by bottom friction in the tidal current decreases in 

 intensity upwards from the bottom. In regions of complete vertical mixing, 

 the intensity of turbulence is sufficiently great at all depths to ensure efficient 

 mixing. A summer thermocline will be formed, however, if there is a level of 

 minimum turbulence at some intermediate depth, where the vertical eddy 

 diffusion is not adequate to transmit the downward flux of heat without an 

 appreciable temperature gradient developing. The conditions governing the 

 formation of a seasonal thermocline appear to be quite critical and the transi- 

 tion from one regime to the other frequently occurs in a distance of a few miles. 

 Dietrich (1950) j^ointed out that, in the English Channel, the areas with com- 

 plete vertical mixing correspond closely to those where the amplitude of the 

 tidal current exceeds 100 cm/sec. 



The influence of a tidal current on vertical mixing was considered quantita- 

 tively by Hansen (1950), who introduced the Richardson number into the 

 equations of motion and mixing and derived a relation between the density 

 gradient and the coefficient of eddy diffusion. The problem was also considered 

 by Dietrich (1954) in relation to the temperature stratification in different 

 parts of the North Sea. It was assumed that if Ri < 0.5, turbulent mixing was 

 effective but when Bi > 0.5 the vertical turbulence was suppressed sufficiently 

 for a temperature gradient to persist. The critical density gradient dp/dz, 

 corresponding to Ri = 0.5, was determined as a function of depth, taking the 

 vertical variation of velocity to follow the power law 



V = vo{zlh)", 



where 1^0 = velocity at surface, 2 = depth below surface, A = total depth and the 

 index a has a value between ^ and y. The critical gradient was compared with 

 that which corresponded to the temperature gradient associated with the 

 downward flux of heat under conditions of summer heating. 



The intensity of turbulence existing in a current also affects the concentration 

 of sediment which it is able to maintain in suspension. This problem has 

 received considerable attention, experimentally and theoretically, in hydraulics 

 (e.g. Vanoni, 1946; Hunt, 1954). Joseph (1954) made a study of the effects of 

 current velocity and stability on the concentration of suspended particles and 

 the optical extinction coefficients at two stations off Texel, in the southern 

 North Sea, A theoretical treatment was given, relating the eddy dififusivity to 

 the particle concentration, and values of Kz were derived which were of the 

 order of 100 cm^/sec near the bottom and 200 cm^/sec near the surface in 

 homogeneous water. When a thermocline was present, the value of Kz near 

 the bottom was reduced only slightly but its value decreased to the order of 

 10 cm2/sec in the discontinuity layer. 



5. Horizontal Turbulence 



The dynamical effect of horizontal turbulence has received most attention in 

 relation to the major ocean currents of the wind-driven circulation. Thus Munk 



27— s, I 



