Related papers: Enhanced dissipation and Taylor dispersion by a pa…
We consider the evolution of a passive scalar advected by a parallel shear flow in an infinite cylinder with bounded cross section, in arbitrary space dimension. The essential parameters of the problem are the molecular diffusivity $\nu$,…
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…
In this note, we study the long-time dynamics of passive scalars driven by rotationally symmetric flows. We focus on identifying precise conditions on the velocity field in order to prove enhanced dissipation and Taylor dispersion in…
We consider a simple model of the evolution of the concentration of a tracer, subject to a background shear flow by a fluid with viscosity $\nu \ll 1$ in an infinite channel. Taylor observed in the 1950's that, in such a setting, the tracer…
We examine the phenomenon of enhanced dissipation from the perspective of H\"ormander's classical theory of second order hypoelliptic operators [31]. Consider a passive scalar in a shear flow, whose evolution is described by the…
This paper investigates enhanced dissipation for a passive scalar advected by "very rough" horizontal shear flows, described by an advection-diffusion equation on the 2D torus. The authors extend results of Galeati and Gubinelli (2023) to…
We analyze the decay and instant regularization properties of the evolution semigroups generated by two-dimensional drift-diffusion equations in which the scalar is advected by a shear flow and dissipated by full or partial diffusion. We…
We develop a theory of enhanced diffusivity and skewness of the longitudinal distribution of a diffusing tracer advected by a periodic time-varying shear flow in a straight channel. Although applicable to general fluid flow, we restrict the…
The phenomenon of Taylor or shear-induced dispersion of a non-passive scalar field in a pulsatile pipe flow is investigated, accounting for the scalar field's influence on fluid density and transport coefficients. By employing multiple…
Taylor diffusion (or dispersion) refers to a phenomenon discovered experimentally by Taylor in the 1950s where a solute dropped into a pipe with a background shear flow experiences diffusion at a rate proportional to $1/\nu$, which is much…
We prove a stability threshold theorem for 2D Navier-Stokes on three unbounded domains: the whole plane $\mathbb{R} \times \mathbb{R}$, the half plane $\mathbb{R} \times [0,\infty)$ with Navier boundary conditions, and the infinite channel…
This work investigates the long-time asymptotic behavior of a diffusing passive scalar advected by fluid flow in a straight channel with a periodically varying cross-section. The goal is to derive an asymptotic expansion for the scalar…
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…
We consider viscous steady streaming induced by oscillatory flow past a cylinder between two plates, where the cylinder's axis is normal to the plates. While this phenomenon was first studied in the 1930s, it has received renewed interest…
We report a non-perturbative study of the effects of shear flows on turbulence reduction in a decaying turbulence in two dimensions. By considering different initial power spectra and shear flows (zonal flows, combined zonal flows and…
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…
We present an exact analytical solution to the problem of shear dispersion given a general initial condition. The solution is expressed as an infinite series expansion involving Mathieu functions and their eigenvalues. The eigenvalue system…
We generalize classical dispersion theory for a passive scalar to derive an asymptotic long-time convection-diffusion equation for a solute suspended in a wide, structured channel and subject to a steady low-Reynolds-number shear flow. Our…
Enhanced diffusion, which describes the accelerated spread of passive scalars due to the interaction between advection and molecular diffusion, has been extensively studied in simplified geometries, such as uniform shear and radial flows.…
We propose a model for the nonequilibrium enhancement of colloidal self-diffusion in an externally imposed shear flow in charged systems. The enhancement of diffusion is calculated in terms of the electrostatic, two--body interactions…