Related papers: Exponential mixing by random cellular flows
In many astrophysical environments, mixing of heavy elements occurs in the presence of a supersonic turbulent velocity field. Here we carry out the first systematic numerical study of such passive scalar mixing in isothermal supersonic…
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,…
We derive an analytical solution for the one-point distribution of a passive scalar in decaying homogeneous turbulence, in the limit of strong turbulence (high Re, fixed Schmidt number). Velocity statistics are governed by the Euler…
We prove a version of Bressan's mixing conjecture where the advecting field is constrained to be a shear at each time. Also, inspired by recent work of Blumenthal, Coti Zelati and Gvalani, we construct a particularly simple example of a…
We present results of direct numerical simulations of passive scalar advection and diffusion in turbulent rotating flows. Scaling laws and the development of anisotropy are studied in spectral space, and in real space using an axisymmetric…
We construct incompressible velocity fields that exhibit faster than exponential dissipation for particular solutions to the advection-diffusion equation on $\mathbb{T}^d$. In 2D, we construct a velocity field in $L^\infty_{t,x}$ and…
Direct numerical simulation data show that the variance of the coupling term in passive scalar advection by a random velocity field is smaller than it would be if the velocity and scalar fields were statistically independent. This effect is…
We revisit the well-known problem of multiscaling in substances passively advected by homogeneous and isotropic turbulent flows or passive scalar turbulence. To that end we propose a two-parameter continuum hydrodynamic model for an…
We consider the persistence phenomenon in advectecd passive scalar equation in 1-dimension. The velocity field is random with the $<v(k,\omega)v(-k,-\omega) > \sim |k|^{-(2+\alpha)}$. In presence of the non-linearity the complete Green's…
We consider a passive scalar that is advected by a prescribed mean zero divergence-free velocity field, diffuses, and reacts according to a KPP-type nonlinear reaction. We introduce a quantity, the bulk burning rate, that makes both…
We consider the advection-diffusion equation on $\mathbb{T}^2$ with a Lipschitz and time-periodic velocity field that alternates between two piecewise linear shear flows. We prove enhanced dissipation on the timescale $|\log \nu|$, where…
We consider the negative regularity mixing properties of random volume preserving diffeomorphisms on a compact manifold without boundary. We give general criteria so that the associated random transfer operator mixes $H^{-\delta}$…
In this paper, we consider the passive scalar solutions in shear flows with critical points. With a detailed hypocoercivity functional, we develop streamline-wise enhanced dissipation estimates.
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 establish a new criterion for exponential mixing of random dynamical systems. Our criterion is applicable to a wide range of systems, including in particular dispersive equations. Its verification is in nature related to several topics,…
Recent numerical results show that if a scalar is mixed by periodically forced turbulence, the average mixing rate is directly affected for forcing frequencies small compared to the integral turbulence frequency. We elucidate this by an…
Expressions for local discrete variance decay (DVD) rates are directly derived from discrete tracer equations without any assumptions on discrete fluxes of the second moment. Spurious mixing (SM) associated with numerical implementations of…
This study is concerned with the diffusion of a passive scalar $\Theta(\r,t)$ advected by general $n$-dimensional shear flows $\u=u(y,z,...,t)\hat{x}$ having finite mean-square velocity gradients. The unidirectionality of the incompressible…
This paper explores the phenomena of enhanced dissipation and Taylor dispersion in solutions to the passive scalar equations subject to time-dependent shear flows. The hypocoercivity functionals with carefully tuned time weights are applied…
Passive scalars advected by a magnetically driven two-dimensional turbulent flow are analyzed using methods of statistical topography. The passive tracer concentration is interpreted as the height of a random surface and the scaling…