The convection of large and intermediate scale fluctuations in a turbulent mixing layer

Abstract

The convection velocity of large and intermediate scale velocity fluctuations in a nominally two-dimensional planar mixing layer, and its dependence upon the length scale, is explored by carrying out particle image velocimetry (PIV) experiments. A “global” convection velocity, containing the convection of all the length scales present in the flow, is produced by examining the autocorrelation functions between velocity fluctuations in successive PIV records across the mixing layer. This “global” convection velocity is found to be similar to the mean flow, although fluctuations on the low speed side of the mixing layer on average convect at speeds greater than the mean and fluctuations on the high speed side of the mixing layer are observed to convect at speeds less than the mean. Scale specific convection velocity profiles are then produced by examining the phase difference between the spectral content specific to one wavenumber in streamwise velocity fluctuation traces in successive PIV records, offset by time τ. Probability density functions (pdfs) are produced of this phase difference, which is subsequently converted into a convection displacement, and these show that the convection of single length scale fluctuations exhibits a significant variance, particularly so for larger scale fluctuations and in the high speed side of the mixing layer. Convection velocity profiles are produced from these pdfs using both the mean convection distance and the modal convection distance. It is observed that the convection velocity is relatively insensitive to the length scale of the fluctuations considered, particularly when the mean convection distance is used. A slight sensitivity to length scale is, however, observed for convection velocities based on the modal convection distance. This dependence is primarily observed in the high speed side of the mixing layer, in which smaller length-scale fluctuations convect more quickly than larger length-scale fluctuations. It is also observed that the magnitude of the fluctuation itself affects the convection velocity with larger magnitude fluctuations convecting less rapidly than lower magnitude ones at the largest length scales investigated with this behaviour being reversed at more intermediate length scales.