Redefining Mixing Length in Turbulent Mixing Layer in Terms of Shear-Induced Vorticity

An incompressible turbulent planar mixing layer is composed of two different flow types in its flow field, namely a shear layer in the central region and two free streams in each outer high- and low-speed sides. Shear layer is formed right after the trailing edge of the splitter plate and develops stream-wisely through successively distinct regions, namely the near field region and the self-preserving region. A new definition of the mixing length (lω) is proposed on the basis of an effectively pure shear-induced vorticity component (ΩSH) by means of a triple decomposition method, that is, lω = yH - yL where yH and yL are the two transverse positions, at which |ΩSH| normalized with the maximum ∂U/∂y at the virtual origin is equal to 0.05, in the high- and low-speed free stream sides, respectively. It is shown that the linear growth rate of lω along stream-wise distance can be, then, used as one of the necessary and sufficient conditions for identifying the achievement of the self-preserving state in turbulent mixing layer.