Gravitational Diffusion From a Boundary Source in Two-Dimensional Flow

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Abstract
Convection currents of heated air downwind from a continuous line of gasoline burners at ground level provided an important means of dispersing fog over airfields during the recent war. A study of heat requirements as a function of burner location and cross-wind velocity, conducted by the Iowa Institute of Hydraulic Research in 1943, yielded results which are considered applicable to all similar problems of gravitational diffusion from a boundary source—such, for instance, as the mixing through induced convection of sediment-laden water introduced at the upper surface of a stream. The author presents herewith a general analysis of the problem, based upon solution of the differential equations of energy and diffusion for the assumption of (1) an error distribution of the specific-weight difference over any normal section and (2) a direct proportionality between the mixing length and the standard deviation of the error curve. Experimental results are shown to verify the analysis with good approximation.

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