The influence of the vorticity-scalar correlation on mixing

We investigate the role of the correlation between a scalar quantity and the vorticity in two-dimensional mixing at infinite P\'eclet number. We assess, using a diffusivity independent mixing-norm, the dynamics of both Galerkin-truncated ensembles and freely evolving two-dimensional scalar mixing. Both statistical mechanics and numerical experiments show how the mixing-rate is attenuated when vorticity and scalar are initially correlated. Since the vorticity is shown to be a poorly mixing scalar, the results suggest that, in general, mixing can be enhanced by minimizing the correlation between vorticity and passive scalar.