A necessary and sufficient condition for enhanced dissipation under transport noise is the absence of non-trivial finite-dimensional invariant subspaces, with sharp rates for stochastic shear flows.
Stabilization by transport noise and enhanced dissipation in the Kraichnan model
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abstract
Stabilization and sufficient conditions for mixing by stochastic transport are shown. More precisely, given a second order linear operator with possibly unstable eigenvalues on a smooth compact Riemannian manifold, it is shown that the inclusion of transport noise can imply global asymptotic stability. Moreover, it is shown that an arbitrary large exponential rate of convergence can be reached, implying enhanced dissipation. The sufficient conditions are shown to be satisfied by the so-called Kraichnan model for stochastic transport of passive scalars in turbulent fluids. In addition, an example is given showing that it can be sufficient to force four modes in order to induce stabilization.
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A Stochastic RAGE Theorem and Enhanced Dissipation for Transport Noise
A necessary and sufficient condition for enhanced dissipation under transport noise is the absence of non-trivial finite-dimensional invariant subspaces, with sharp rates for stochastic shear flows.