Asymptotic evolution of a passive scalar field advected by an homogeneous turbulent shear flow

The large-time decay of an homogeneous fluctuating scalar field in uniformly sheared homogeneous turbulence is examined following different points of view which are discussed in turn. Self-preservation analysis of the scalar spectrum equation predicts an exponential decrease of the scalar variance and a constant scalar-to-velocity timescale ratio R. One-point approaches reveal the same qualitative behaviour and the few available experimental data appear to agree with this picture. However, current one-point modelling leads to an asymptotic value of R independently from initial conditions and shear whereas this universality is broken down when allowing for residual vortex stretching in both the velocity and the scalar fields. Further insight into the physics and quantitative evaluation of above concepts would require ad hoc measurements.