Dispersivity Tensor for Turbulent Uniform Channel Flow

The turbulent mixing of a solute in a stream flow is described with the aid of the dispersivity tensor. In a two-dimensional pipe or wide channel flow only the radial, or vertical, dispersivity coefficient is significant and is usually determined through the Reynolds analogy. The analogy is extended to a three-dimensional (i.e., channel of arbitrary section) uniform flow. It is shown that the mixing length theory leads to the representation of the dispersivity tensor in the terms of only two distinct coefficients: (1) A coefficient representing mixing normal to isovels which may be found through Reynolds analogy; and (2) a lateral dispersivity coefficient which has to be determined from dispersivity measurements.