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Generalization of the Mixing-Length Argument in Turbulent Diffusion

Gabriel T. CsanadyUniversity of Waterloo, Ontario, Canada

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Abstract

The gradient diffusion hypothesis is replaced by a generalized “mixing-length” type argument, the essence of which is that a drifting particle effectively “originates” some distance from the point where turbulent flux is calculated and carries with itself the mean concentration appropriate to its region of origin. Thus, turbulent flux is set proportional to a weighted integral of the mean concentration distribution. On applying the principle of continuity one obtains an integral equation describing turbulent diffusion. To illustrate the use of this equation, various assumptions are made regarding the coordinates of the effective origin and the development of the concentration profile in the wake of a point source calculated numerically. The results appear to be of interest, but accurate experimental data are required before the theory becomes quantitatively useful.

Abstract

The gradient diffusion hypothesis is replaced by a generalized “mixing-length” type argument, the essence of which is that a drifting particle effectively “originates” some distance from the point where turbulent flux is calculated and carries with itself the mean concentration appropriate to its region of origin. Thus, turbulent flux is set proportional to a weighted integral of the mean concentration distribution. On applying the principle of continuity one obtains an integral equation describing turbulent diffusion. To illustrate the use of this equation, various assumptions are made regarding the coordinates of the effective origin and the development of the concentration profile in the wake of a point source calculated numerically. The results appear to be of interest, but accurate experimental data are required before the theory becomes quantitatively useful.

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