Related papers: Exponential mixing by random cellular flows
We study anomalous dissipation in the context of passive scalars and we construct a two-dimensional autonomous divergence-free velocity field in $C^\alpha$ (with $\alpha \in (0,1)$ arbitrary but fixed) which exhibits anomalous dissipation.…
The scalar field with an exponential potential allows a scaling solution where the the density of the field follows the density of the dominating fluid. Such a scaling regime is often used as an important ingredient in many models of…
We numerically investigated the dynamics of a mixture of finite-size active and passive particles in a linear array of convection rolls. The interplay of advection and steric interactions produces a number of interesting effects, like the…
We analyze the dynamics of solute mixing in a vortex flow. The transport of a passive tracer is considered in a Rankine vortex. The action of a shear flow, in general, is to achieve stretching of fluid elements. A vortex flow exhibits…
We investigate the role of the correlation between a scalar quantity and the vorticity in two-dimensional mixing at infinite P\'eclet number. We assess, using a diffusivity independent mixing-norm, the dynamics of both Galerkin-truncated…
The motions of a passive scalar $\hat{a}$ in a general high-frequency oscillating flow are studied. Our aim is threefold: (i) to obtain different classes of general solutions; (ii) to identify, classify, and develop related asymptotic…
We quantitatively study the mixing rate of randomly shifted alternating shears on the torus. This flow was introduced by Pierrehumbert '94, and was recently shown to be exponentially mixing. In this work, we quantify the dependence of the…
We consider a solvable model of the decay of scalar variance in a single-scale random velocity field. We show that if there is a separation between the flow scale k_flow^{-1} and the box size k_box^{-1}, the decay rate lambda ~…
In this paper, we consider an exponential scalar auxiliary variable (E-SAV) approach to obtain energy stable schemes for a class of phase field models. This novel auxiliary variable method based on exponential form of nonlinear free energy…
The mixing effectiveness, i.e., the enhancement of molecular diffusion, of a flow can be quantified in terms of the suppression of concentration variance of a passive scalar sustained by steady sources and sinks. The mixing enhancement…
The compressibility and heat of reaction influence on the scalar mixing in decaying isotropic turbulence and homogeneous shear flow are examined via data generated by direct numerical simulations (DNS). The reaction is modeled as one-step,…
We investigate the large-scale statistics of a passive scalar transported by a turbulent velocity field. At scales larger than the characteristic lengthscale of scalar injection, yet smaller than the correlation length of the velocity, the…
We develop a framework for studying the enhanced dissipation of passive scalars advected by shear flows based on analyzing the particle trajectories of the stochastic differential equation associated with the governing drift-diffusion…
To understand how spatiotemporal chaos may modify material transport, we use direct numerical simulations of the three-dimensional Boussinesq equations and of an advection-diffusion equation to study the transport of a passive tracer by the…
The diffusive properties in velocity fields whose small scales are parameterized by non $\delta$-correlated noise is investigated using multiscale technique. The analytical expression of the eddy diffusivity tensor is found for a 2D steady…
We use direct numerical simulations to compute structure functions, scaling exponents, probability density functions and turbulent transport coefficients of passive scalars in turbulent rotating helical and non-helical flows. We show that…
We use a custom shear cell coupled to an optical microscope to investigate at the particle level the yielding transition in concentrated emulsions subjected to an oscillatory shear deformation. By performing experiments lasting thousands of…
Recent experimental results indicate that mixing is enhanced by a reciprocal flow induced inside a levitated droplet with an oscillatory deformation [T. Watanabe et al. Sci. Rep. 8, 10221 (2018)]. Generally, reciprocal flow cannot convect…
We establish rigorous lower bounds on the speed of traveling fronts and on the bulk burning rate in reaction-diffusion equation with passive advection. The non-linearity is assumed to be of either KPP or ignition type. We consider two main…
We consider the linear growth-fragmentation equation arising in the modelling of cell division or polymerisation processes. For constant coefficients, we prove that the dynamics converges to the steady state with an exponential rate. The…