






















We consider the mixing properties of solutions to the advection-diffusion equation of a white-in-time velocity field on the 2-dimensional torus with four forced modes. As the diffusivity parameter goes to zero, we show that the almost-sure exponential dissipation rate stays bounded from below. Together with the corresponding upper bound established by Gess and Yaroslavtsev, this constitutes an example of a velocity field for which the Batchelor scale conjecture can be verified. In addition, we characterize the exponential mixing rate without diffusion of this system. Our results are not restricted to two dimensions, and we construct a three-dimensional white-in-time velocity field with the same properties.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。