Comparison of backwards and forwards scalar relative dispersion in turbulent shear flow

Turbulent mixing is characteristically identifiable with backwards relative dispersion, where pairs of particles get transported to the mixing location. However, relative dispersion models are insensitive to this fact and predominantly apply forwards relative dispersion concepts. The goal of the current study is to highlight and interpret differences, if any, between the forwards and backwards relative dispersion. Direct numerical simulation is used to obtain the flow field in an infinitely long channel. A Lagrangian technique is used in conjunction with the direct numerical simulation to track scalar markers released into this flow field. Two different types of flow, Poiseuille channel flow, where the walls of the channel are stationary, and plane Couette flow, where the walls of the channel move in opposite directions relative to each other, are simulated. Forwards relative dispersion is found to be faster in the viscous sub-layer, the transition region and the logarithmic regions of the Poiseuille channel flow, while the backwards relative dispersion is faster in the center of the channel. Faster forwards relative dispersion is seen in the center of the Couette flow channel and the logarithmic region, while higher rate of backwards relative dispersion is observed in the viscous sub-layer and the transition region. The underlying reason for differences in relative dispersion is related to the turbulence velocity structure and the velocity fluctuation probability density function that the particle pairs experience while traveling towards or away from a point. It is also found that the Prandtl number affects rates of forwards and backwards relative dispersion in a systematic manner.