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Published November 1990 | Published
Journal Article Open

Some consequences of the boundedness of scalar fluctuations


Values of the scalar field c(x,t), if initially bounded, will always be bounded by the limits set by the initial conditions. This observation permits the maximum variance ∼(c′^2) to be computed as a function of the mean value c. It is argued that this maximum should be expected in the limit of infinite Schmidt numbers (zero scalar species diffusivity). This suggests that c′/c on the axis of turbulent jets, for example, may not tend to a constant, i.e., independent of x/d, in the limit of very large Schmidt numbers. It also underscores a difficulty with the k^(−1) scalar spectrum proposed by Batchelor [J. Fluid Mech. 5, 113 (1959)].

Additional Information

© 1990 American Institute of Physics. Received 24 August 1990; accepted 11 September 1990. We would like to acknowledge our discussions with P. Saffman, D. Meiron, and H. K. Moffatt. This work is part of a larger effort on turbulent mixing supported by AFOSR Grant No. 88-0155 and GRI Contract No. 5087-260-1467.

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