We consider parallel mixing by advection and diffusion modelled by the linear advection-diffusion equation for general velocity fields with bounded enstrophy. We present optimal estimates on the rates of decay of the $L^2$ norm, which describes the phenomenon of enhanced dissipation, and we deduce bounds on the rates of decay of the $H^{-1}$ norms, which describes the effect of mixing. The results show that the optimal time scales for both phenomena are of the order of a logarithm of the diffusivity constant.
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