Passive Advection and the Degenerate Elliptic Operators $M_n$

Noise prevents infinite stretching of the passive field in a stochastic vector advection equation

A linear stochastic vector advection equation is considered; the equation may model a passive magnetic field in a random fluid. When the driving velocity field is rough but deterministic, in particular just Hölder continuous and bounded, one can construct examples of infinite stretching of the passive field, arising from smooth initial conditions. The purpose of the paper is to prove that infinite stretching is prevented if the driving velocity field contains in addition a white noise component.

特殊随机标度极限下被动标量与矢量平流方程的背景Vlasov方程和Young测度

Background Vlasov equations and Young measures for passive scalar and vector advection equations under special stochastic scaling limits

该研究针对随机标度极限下被动标量与矢量平流方程，引入背景随机Vlasov方程，证明其收敛到满足带扩散项极限PDE的非平凡Young测度，为被动矢量场情形的随机平流方程提供了新的统计信息。

Advection of passive particles over flow networks

The problem of stochastic advection of passive particles by circulating conserved flows on networks is formulated and investigated. The particles undergo transitions between the nodes with the transition rates determined by the flows passing through the links. Such stochastic advection processes lead to mixing of particles in the network and, in the final equilibrium state, concentration of particles in all nodes become equal. As we find, equilibration begins in the subset of nodes, representing flow hubs, and extends to the periphery nodes with weak flows. This behavior is related to the effe…

粗糙Kraichnan流中的被动标量平流模拟

Simulating passive scalar advection in rough Kraichnan flows

本研究通过欧拉式伪谱方法模拟粗糙二维Kraichnan流中的被动标量平流，验证相关标度律，明确模拟参数随速度粗糙度指数的调整规则，为Kraichnan模型扩展形式的模拟提供数值基准。

Helical turbulent Prandtl number in the $A$ model of passive advection: Two loop approximation

Using the field theoretic renormalization group technique in the two-loop approximation, turbulent Prandtl numbers are obtained in the general $A$ model of passive vector advected by fully developed turbulent velocity field with violation of spatial parity introduced via continuous parameter $ρ$ ranging from $ρ=0$ (no violation of spatial parity) to $|ρ|=1$ (maximum violation of spatial parity). In non-helical environments, we demonstrate that $A$ is restricted to $-1.723 \leq A \leq 2.800$ (rounded on the last presented digit) due to the constraints of two-loop calculations. When $ρ>0.749$ re…

A Lagrangian perspective on nonautonomous advection-diffusion processes in the low-diffusivity limit

We study mass preserving transport of passive tracers in the low-diffusivity limit using Lagrangian coordinates. Over finite-time intervals, the solution-operator of the nonautonomous diffusion equation is approximated by that of a time-averaged diffusion equation. We show that leading order asymptotics that hold for functions [Krol, 1991] extend to the dominant nontrivial singular value. This answers questions raised in [Karrasch & Keller, 2020]. The generator of the time-averaged diffusion/heat semigroup is a Laplace operator associated to a weighted manifold structure on the material manifo…