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Creators/Authors contains: "Cooperman, William"

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  1. ; ; (, Nonlinearity)
    Abstract In many situations, the combined effect of advection and diffusion greatly increases the rate of convergence to equilibrium—a phenomenon known asenhanced dissipation. Here we study the situation where the advecting velocity field generates a random dynamical system satisfying certainHarris conditions. Ifκdenotes the strength of the diffusion, then we show that with probability at least 1 − o ( κ N ) enhanced dissipation occurs on time scales of order | ln ⁡ κ | , a bound which is known to be optimal. Moreover, on long time scales, we show that the rate of convergence to equilibrium is almost surelyindependentof diffusivity. As a consequence we obtain enhanced dissipation for the randomly shifted alternating shears introduced by Pierrehumbert’94. 
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