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 mod el the evolution of a blob of turbulent kinetic energy under the influence of production, dissipation, and transport, as well as distortion by the mea n motion. A single length-scale is defined which is biased toward the small est of the scales in the various directions. Constants are estimated by con sideration of homogeneous decay. Preliminary computations are carried out i n a mixing layer and a two-dimensional jet, using the new length-scale equa tion and the equation for the turbulent kinetic energy. The results are com pared with data and with the predictions of the classical k-epsilon equatio ns; the new results are quite satisfactory. In particular, the plane jet/ro und jet anomaly is approximately resolved.