Determination of mixing length in turbulent mixing layer on basis of vorticity field

Vorticity dynamics plays an essential role in the description of turbulent flows, so an alternative definition of the mixing length (l_ω=y_H−y_L where y_H and y_L represent the transverse boundary positions of turbulent shear layer at the high- and low-speed free streams, respectively) in a turbulent planar mixing layer, based on the shear induced vorticity field, is suggested in this study. A theoretical analysis for determining the values of y_H and y_L in the self-preserving development region is presented. An experimental study that demonstrates the self-preserving state in planar turbulent mixing layer is next made with particle image velocimetry (PIV) measurements to support the theoretical results. It is shown that “a linear growth rate of l_ω along stream-wise distance” can be now used as the necessary and sufficient conditions to identify the achievement of a self-preserving state in a turbulent mixing layer. Another advantage of this alternative definition of mixing length is that l_ω gives a better sectional range of shear turbulence in a turbulent mixing layer than the usual definitions of mixing length, which are determined on the basis of the mean velocity field, such as l_u.