Related papers: Cellular mixing with bounded palenstrophy
Mixing is relevant to many areas of science and engineering, including the pharmaceutical and food industries, oceanography, atmospheric sciences, and civil engineering. In all these situations one goal is to quantify and often then to…
We are concerned with flow enhanced mixing of passive scalars in the presence of diffusion. Under the assumption that the velocity gradient is suitably integrable, we provide upper bounds on the exponential rates of enhanced dissipation.…
We study passive scalar mixing by parallel shear flows in the presence of weak molecular diffusion. We recover the sharp uniform-in-diffusivity mixing rate for shear flows with finitely many critical points, recently proven in [1]. Our…
Mixing in open incompressible flows is studied in a model problem with inhomogeneous passive scalar injection on an inlet boundary. As a measure of the efficiency of stirring, the bulk scalar concentration variance is bounded and the bound…
In this article we are interested in the geometric and analytic mixing scales of solutions to passive scalar problems. Here, we show that both notions are comparable after possibly removing large scale projections. In order to discuss our…
The mixing efficiency of a flow advecting a passive scalar sustained by steady sources and sinks is naturally defined in terms of the suppression of bulk scalar variance in the presence of stirring, relative to the variance in the absence…
We study the dynamics of seeded plasma blobs and depletions in an (effective) gravitational field. For incompressible flows the radial center of mass velocity of blobs and depletions is proportional to the square root of their initial…
Mixing of passive scalars in compressible turbulence does not obey the same classical Reynolds number scaling as its incompressible counterpart. We first show from a large database of direct numerical simulations that even the solenoidal…
Collective cell flows are a hallmark of tissue dynamics in development, wound healing, and various diseases. Here, we perform experiments on epithelial MDCK cell monolayers, over tens of hours without jamming, on millimeter-scale…
Multiscale mixing efficiencies for passive scalar advection are defined in terms of the suppression of variance weighted at various length scales. We consider scalars maintained by temporally steady but spatially inhomogeneous sources,…
High-resolution large-eddy simulations of decaying stratified and unstratified homogeneous turbulence are used to understand the mixing of passive scalars in stably stratified flows. Two passive scalar mixing layers, one in the vertical…
We study the passive transport of a scalar field by a spatially smooth but white-in-time incompressible Gaussian random velocity field on $\mathbb{R}^d$. If the velocity field $u$ is homogeneous, isotropic, and statistically self-similar,…
We demonstrate that at long times the rate of passive scalar decay in a turbulent, or simply chaotic, flow is dominated by regions (in real space or in inverse space) where mixing is less efficient. We examine two situations. The first is…
We deal with the problem of separation of time-scales and filamentation in a linear drift-diffusion problem posed on the whole space $\mathbb{R}^2$. The passive scalar considered is stirred by an incompressible flow with radial symmetry. We…
We study the mixing of active scalars by homogeneous isotropic incompressible stochastic velocity fields. We consider both Navier-Stokes generated turbulent fields as well as artificially generated homogeneous isotropic stochastic fields.…
The joint probability density function (PDF) of turbulent velocity and concentration of a passive scalar in an urban street canyon is computed using a newly developed particle-in-cell Monte Carlo method. Compared to moment closures, the PDF…
Mixing-via-shearing is a powerful and versatile method for establishing mixing properties of smooth parabolic flows. In its quantitative form, it provides upper bounds on the decay of correlations for sufficiently smooth observables.…
The interchange dynamics and velocity scaling of blob-like plasma filaments are investigated using a two-field reduced fluid model. For incompressible flows due to buoyancy the maximum velocity is proportional to the square root of the…
Mixing in viscous fluids is challenging, but chaotic advection in principle allows efficient mixing. In the best possible scenario,the decay rate of the concentration profile of a passive scalar should be exponential in time. In practice,…
The mixing of passive scalars of decreasing diffusivity, advected in each case by the same three-dimensional Navier-Stokes turbulence, is studied. The mixing becomes more isotropic with decreasing diffusivity. The local flow in the vicinity…