Related papers: Dispersion and reaction in random flows: single re…
We present a generalization of turbulent pair dispersion to large initial separations ($\eta < r_0 < L$), by introducing a new time scale, $\tau_{v_0}$, that reflects the persistence of initial conditions at time $\tau=0$. Results of 3D…
The dispersion of a passive scalar in an axially strained flow in a slender tube is studied, with particular focus on large-time asymptotics following the approach of~\cite{rajamanickam2020dispersion}. For times exceeding the…
The analysis of the radial distribution function of a system provides a possible procedure for uncovering interaction rules between individuals out of collective movement patterns. This approach from classical statistical mechanics has…
We study the long-time behavior of a particle in $\mathbb{R}^d$, $d \geq 2$, subject to molecular diffusion and advection by a random incompressible flow. The velocity field is the divergence of a stationary random stream matrix $\mathbf{k}…
We study enhancement of diffusive mixing on a compact Riemannian manifold by a fast incompressible flow. Our main result is a sharp description of the class of flows that make the deviation of the solution from its average arbitrarily small…
Passive scalar turbulence forced steadily is characterized by the velocity correlation scale, $L$, injection scale, $l$, and diffusive scale, $r_d$. The scales are well separated if the diffusivity is small, $r_d\ll l,L$, and one normally…
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…
The turbulent diffusion of Lagrangian tracer particles has been studied in a flow on the surface of a large tank of water and in computer simulations. The effect of flow compressibility is captured in images of particle fields. The velocity…
In a recent work on fluid infiltration in a Hele-Shaw cell with the pore-block geometry of Sierpinski carpets (SCs), the area filled by the invading fluid was shown to scale as F~t^n, with n<1/2, thus providing a macroscopic realization of…
We present exact spatio-temporal correlation functions of a Rouse polymer chain submerged in a fluid having planar mixed flow, in the steady state. Using these correlators, determination of the time scale distribution functions associated…
Single-file systems, in which particles diffuse in narrow channels while not overtaking each other, is a fundamental model for the tracer subdiffusion observed in confined geometries, such as in zeolites or carbon nanotubes. Twenty years…
The dispersion of solute in porous media shows a non-linear increase in the transition from diffusion to advection dominated dispersion as the flow velocity is raised. In the past, the behavior in this intermediate regime has been explained…
In this paper, we investigate the long-time behavior of a passive scalar advected by a parallel shear flow in an infinite cylinder with unbounded cross section, in the regime where the viscosity coefficient satisfies $\nu \ll 1$, and in…
The Obukhov-Corrsin theory of scalar turbulence [Obu49, Cor51] advances quantitative predictions on passive-scalar advection in a turbulent regime and can be regarded as the analogue for passive scalars of Kolmogorov's K41 theory of fully…
The field theoretic renormalization group and operator product expansion are applied to the problem of a passive scalar advected by the Gaussian nonsolenoidal velocity field with finite correlation time, in the presence of large-scale…
We discuss chaotic advection in three-dimensional unsteady incompressible laminar flow, and analyse in detail the most important novel advection phenomenon in these flows; the global dispersion of passive scalars in flows with two slow and…
Since the pioneering work of Richardson in 1926, later refined by Batchelor and Obukhov in 1950, it is predicted that the rate of separation of pairs of fluid elements in turbulent flows with initial separation at inertial scales, grows…
We investigate experimentally the statistical properties of active and passive scalar fields in turbulent Rayleigh-B\'{e}nard convection in water, at $Ra\sim10^{10}$. Both the local concentration of fluorescence dye and the local…
We introduce and study the first model of an experimentally realizable three-dimensional time-dependent nonturbulent fluid flow to display the phenomenon of global diffusion of passive-scalar particles at arbitrarily small values of the…
We prove the absence of anomalous dissipation for passive scalars driven by some random autonomous divergence-free vector fields in $\mathbb T^d$. In dimension $d=2$ we just need continuity almost surely and a mild nondegeneracy condition…