Modulation of the velocity gradient tensor by concurrent large-scale velocity fluctuations in a turbulent mixing layer

The modulation of small-scale velocity and velocity gradient quantities by concurrent large-scale velocity fluctuations is observed by consideration of the Kullback-Leibler divergence. This is a measure that quantifies the loss of information in modelling a statistical distribution of small-scale quantities conditioned on concurrent positive large-scale fluctuations by that conditioned on negative large-scale fluctuations. It is observed that the small-scale turbulence is appreciably 'rougher' when the concurrent large-scale fluctuation is positive in the low-speed side of a fully developed turbulent mixing layer, which gives further evidence to the convective scale modulation argument of Buxton & Ganapathisubramani (Phys. Fluids, vol. 26, 2014, 125106, 1-19). The definition of the small scales is varied, and regardless of whether the small-scale fluctuations are dominated by dissipation or have the characteristic features of inertial range turbulence they are shown to be modulated by the concurrent large-scale fluctuations. The modulation is observed to persist even when there is a large gap in wavenumber space between the small and large scales, although local maxima are observed at intermediate length scales that are significantly larger than the predefined small scales. Finally, it is observed that the modulation of small-scale dissipation is greater than that for enstrophy with the modulation of the vortex stretching term, indicative of the interaction between strain rate and rotation, being intermediate between the two.