A Length-Scale Equation

We derive an equation for the average length-scale in a turbulent flow from a simple physical model. This is a tensorial length-scale. We use as a model the evolution of a blob of turbulent kinetic energy under the influence of production, dissipation, and transport, as well as distortion by the mean motion. A single length-scale is defined which is biased toward the smallest of the scales in the various directions. Constants are estimated by consideration of homogeneous decay. Preliminary computations are carried out in a mixing layer and a two-dimensional jet, using the new length-scale equation and the equation for the turbulent kinetic energy. The results are compared with data and with the predictions of the classical k-epsilon equations; the new results are quite satisfactory. In particular, the plane jet/round jet anomaly is approximately resolved.