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<p>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.</p>

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Stabilization by transport noise and enhanced dissipation in the Kraichnan model

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月16日

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  • Benjamin Gess,
  • Ivan Yaroslavtsev

摘要

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.