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.
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Yin et al. (2024) studied this question.
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