A method of treating turbulent pair dispersion and scalar diffusion is presented. Use is made of Kraichnan's form of Richardson's diffusion equation by relating the turbulent pair diffusivity to single-time Eulerian velocity statistics (which are presumed known) by means of a statistical independence hypothesis. In this procedure the diffusivity itself is coupled to solutions of the diffusivity equation in a self-consistent way. The method is applied to both two-and three-dimensional flow. In three-dimensional inertial-range and dissipative-range turbulence the turbulent pair diffusivity is determined and used to find the values of the coefficients of the scalar spectrum in the k-5/3 and k−1 ranges with good agreement with experiment. The Obukhov–Corrsin constant is found to be 0·49 and the Batchelor constant is √5. In two-dimensional turbulence the results are compared with constant-pressure balloon dispersion experiments. Results are also found for the rate of decay of scalar intensity in the special case where the initial scalar spectrum peaks in the inertial range.
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T. S. Lundgren (1981) studied this question.
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