Stretching and folding diagnostics in solutions of the three-dimensional Euler and Navier-Stokes equations

Measures of mixing quality in open flows with chaotic advection

We address the evaluation of mixing efficiency in experiments of chaotic mixing inside an open-flow channel. Since the open flow continuously brings new fluid into the limited mixing region, it is difficult to define relevant mixing indices, as fluid particles experience typically very different stretching and mixing histories. The repeated stretching and folding of a spot of dye leads to a persistent pattern. We propose that the normalized standard deviation of this characteristic pattern is a good measure of the mixing quality of the flow. We discuss the link between this measure and mixing …

Fast chemical reaction in two-dimensional Navier-Stokes flow: Initial regime

This paper studies an infinitely fast bimolecular chemical reaction in a two-dimensional bi-periodic Navier-Stokes flow. The reactants in stoichiometric quantities are initially segregated by infinite gradients. The focus is placed on the initial stage of the reaction characterized by a well-defined one dimensional material contact line between the reactants. Particular attention is given to the effect of the diffusion of the reactants. This study is an idealized framework for isentropic mixing in the lower stratosphere and is motivated by the need to better understand the effect of resolution…

Vorticity alignment results for the three-dimensional Euler and Navier-Stokes equations

We address the problem in Navier-Stokes isotropic turbulence of why the vorticity accumulates on thin sets such as quasi-one-dimensional tubes and quasi-two-dimensional sheets. Taking our motivation from the work of Ashurst, Kerstein, Kerr and Gibson, who observed that the vorticity vector ${\boldmath$ω$}$ aligns with the intermediate eigenvector of the strain matrix $S$, we study this problem in the context of both the three-dimensional Euler and Navier-Stokes equations using the variables $α= \hat{\boldmath$ξ$}\cdot S\hat{\boldmath$ξ$}$ and ${\boldmath$χ$} = \hat{\boldmath$ξ$}\times S\hat{\b…

动态多相流引发多孔介质中的混沌混合

Dynamic multiphase flow triggers chaotic mixing in porous media

研究动态两相流对流体元素拉伸和折叠的影响，发现其能引发混沌混合，增强溶质混合效率。

三维纳维-斯托克斯湍流中不确定性的产生

The production of uncertainty in three-dimensional Navier-Stokes turbulence

本研究推导了纳维-斯托克斯湍流中不确定性能量演化方程，通过直接数值模拟发现应变率压缩增加不确定性，并识别出指数增长及后续超指数增长等相似性规律。

Two-way coupling of FENE dumbbells with a turbulent shear flow

We present numerical studies for finitely extensible nonlinear elastic (FENE) dumbbells which are dispersed in a turbulent plane shear flow at moderate Reynolds number. The polymer ensemble is described on the mesoscopic level by a set of stochastic ordinary differential equations with Brownian noise. The dynamics of the Newtonian solvent is determined by the Navier-Stokes equations. Momentum transfer of the dumbbells with the solvent is implemented by an additional volume forcing term in the Navier-Stokes equations, such that both components of the resulting viscoelastic fluid are connected b…

Highly turbulent solutions of LANS-alpha and their LES potential

We compute solutions of the Lagrangian-Averaged Navier-Stokes alpha-model (LANS) for significantly higher Reynolds numbers (up to Re 8300) than have previously been accomplished. This allows sufficient separation of scales to observe a Navier-Stokes (NS) inertial range followed by a 2nd LANS inertial range. The analysis of the third-order structure function scaling supports the predicted l^3 scaling; it corresponds to a k^(-1) scaling of the energy spectrum. The energy spectrum itself shows a different scaling which goes as k^1. This latter spectrum is consistent with the absence of stretching…