An Example of the Diffusion of a Floating Dye Patch in the Sea

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Abstract
The formulae for floating-source type diffusion obtained by Drs. E. INOUE (1952) and Y. OGURA (1952) are as follows : <X2>=<Y2>=<Z2>-εt3 Kx=Ky=Kz-εt2 under the condition that t is not so large and that, consequently, the width is sufficiently smaller than the scale of the largest turbulon existing in the atmosphere. And when the averaging time of observation is larger than the life-time of the largest turbulon the standard deviation of the co-ordinates of particles is giver by <X2>=<Y2>=<Z2>=2<V2>τ0 (t-τ0/3) and the so-called eddy diffusion has a definite meaning such as K=<V2>τ0 The result of observation off Tokai mura is shown in Figs 1, 2 and 3. From Fig. 3, the mean squares of the distance of particles are given by √<X2>-εt0.495 √<Y2>-εt0.75 These results show that there were no large eddies and the life-time of maximum turbulon is small. From the x-wards diffusion, √<X2>=65 (t-20) 1/2, Kx=2113 cm2 sec-1, τ0=60 sec, ∧-346 cm, V-6.1 cm/sec, ε-0.65 cm2 sec-3. The y-wards phenomenon shows it was a transient state that the diffusion width increased in proportion to from 3/2 to 1/2 power of the observing time. Next the visible outline of a floating dye patch and the concentration distribution in the sea are discussed. The maximum value of the contaminated area S0 is obtained at the time t0 and the dye patch disappeared at the time T.

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