SECT. 6] TURBULENCE 821 



Ozmidov (1958a) by analogy with the l'^^^ law, considered it reasonable to take 

 K{r) = cr^^^, which leads to the solution 



^(^' " = mW3 -""•'*«• (36) 



It will be seen that these three solutions give different rates for the decrease 

 of intensity with time at the centre of the patch, and for the decrease of in- 

 tensity with distance from the centre at a given time. Ozmidov (1958a) con- 

 sidered data given by Nan'niti and Okubo (1957) on the dispersion of a drifting 

 patch of dye and found that the rate of decrease of intensity at the centre of 

 the patch followed the t"^ law given by (36). However, Bowles et al. (1958), in 

 the experiment described below, found that, after the first 30 min, the intensity 

 at the centre decreased as t"^, corresponding to a constant Kh. 



Most observations liitherto have been analyzed in terms of a constant Kh 

 but the formulae used can only be valid over a limited range of r and the value 

 of Kh which is derived will increase with the average radius r of the observa- 

 tions. Munk et al. (1949) showed that estimates of Kn made by various authors 

 on a wide range of scales could be represented by an approximately linear 

 relation. The ratio Kh/r lay between 0.2 and 0.5 cm/sec for r ranging from 

 103 cm to 108 cm. Munk et al. investigated the dispersion of radioactivity in 

 Bikini lagoon during the three days following the underwater explosion of an 

 atomic bomb. From the lateral spreading they deduced values oi Ky= 1.5 x 10^ 

 cm2/sec near the surface and 0.5 x 10^ cm^/sec at a depth of 150 ft, which 

 corresponded to Kylr = 0.5 cm/sec approximately. The velocity of drift at 

 150 ft was in the opposite direction to that at the surface and one-third of its 

 magnitude. 



Joseph and Sendner (1958) applied their theory to the data on the diffusion 

 of radioactive matter reported by Folsom and Vine (1957), to the distribution 

 of optical turbidity in the Irminger Sea and the southern North Sea and to 

 the spreading of Mediterranean water in the Atlantic Ocean. They found that 

 their treatment, with K{r) — Pr, was valid for values of r ranging from 10 km to 

 1500 km, with P having the common value of 1 cm/sec + 0.5 cm/sec. P may be 

 interpreted as the most probable "diffusion velocity", r/t, where r is the dis- 

 tance from the origin reached by a diffusing particle after time t. The equivalent 

 value of K, assumed constant, computed from the same data, would give 

 K = Prl2, so that P=l cm/sec corresponds to the value of Kh/r — 0.5 cm/sec 

 given by Munk et al. (1949). 



Observations of the diffusion of dye patches in coastal waters in the presence 

 of fairly strong tidal currents have been described by Seligman (1956) and 

 Bowles et al. (1958). They found that the effective diflfusivity increased with 

 the velocity of the tidal current and was considerably larger in the direction of 

 the current {Kx) than transverse to it (Ky). Thus Bowles et al. found, in an 

 area of the English Channel, mean values of Kx=l.8xl0^ cm^/sec, Ky = 

 1.1 X 10^ cm2/sec in a mean current of 1 knot (51.5 cm/sec). They attributed the 

 large value of Kx to the "shear effect", associated with the vertical gradient of 



