On the dynamical origin of asymptotic t^2 dispersion of a nondiffusive tracer in incompressible laminar flows

Using an elementary application of Birkhoff's ergodic theorem, necessary and sufficient conditions are given for the existence of asymptotically t^2 dispersion of a distribution of nondiffusive passive tracer in a class of incompressible laminar flows. Nonergodicity is shown to be the dynamical mechanism giving rise to this behavior

Front propagation in laminar flows

The problem of front propagation in flowing media is addressed for laminar velocity fields in two dimensions. Three representative cases are discussed: stationary cellular flow, stationary shear flow, and percolating flow. Production terms of Fisher-Kolmogorov-Petrovskii-Piskunov type and of Arrhenius type are considered under the assumption of no feedback of the concentration on the velocity. Numerical simulations of advection-reaction-diffusion equations have been performed by an algorithm based on discrete-time maps. The results show a generic enhancement of the speed of front propagation by the underlying flow. For small molecular diffusivity, the front speed $V_f$ depends on the typical flow velocity $U$ as a power law with an exponent depending on the topological properties of the flow, and on the ratio of reactive and advective time-scales. For open-streamline flows we find always $V_f \sim U$, whereas for cellular flows we observe $V_f \sim U^{1/4}$ for fast advection, and $V_f \sim U^{3/4}$ for slow advection.Comment: Enlarged, revised version, 37 pages, 14 figure

Estimating eddy diffusivities from noisy Lagrangian observations

The problem of estimating the eddy diffusivity from Lagrangian observations in the presence of measurement error is studied in this paper. We consider a class of incompressible velocity fields for which is can be rigorously proved that the small scale dynamics can be parameterised in terms of an eddy diffusivity tensor. We show, by means of analysis and numerical experiments, that subsampling of the data is necessary for the accurate estimation of the eddy diffusivity. The optimal sampling rate depends on the detailed properties of the velocity field. Furthermore, we show that averaging over the data only marginally reduces the bias of the estimator due to the multiscale structure of the problem, but that it does significantly reduce the effect of observation error

Clustering and Turbophoresis in a Shear Flow without Walls

We investigate the spatial distribution of inertial particles suspended in the bulk of a turbulent inhomogeneous flow. By means of direct numerical simulations of particle trajectories transported by the turbulent Kolmogorov flow, we study large and small scale mechanisms inducing inhomogeneities in the distribution of heavy particles. We discuss turbophoresis both for large and weak inertia, providing heuristic arguments for the functional form of the particle density profile. In particular, we argue and numerically confirm that the turbophoretic effect is maximal for particles of intermediate inertia. Our results indicate that small-scale fractal clustering and turbophoresis peak in different ranges in the particles' Stokes number and the separation of the two peaks increases with the flow's Reynolds number.Comment: 13 pages, 5 figure

Cytoplasmic Flow and Mixing Due to Deformation of Motile Cells.

The cytoplasm of a living cell is a dynamic environment through which intracellular components must move and mix. In motile, rapidly deforming cells such as human neutrophils, bulk cytoplasmic flow couples cell deformation to the transport and dispersion of cytoplasmic particles. Using particle-tracking measurements in live neutrophil-like cells, we demonstrate that fluid flow associated with the cell deformation contributes to the motion of small acidic organelles, dominating over diffusion on timescales above a few seconds. We then use a general physical model of particle dispersion in a deforming fluid domain to show that transport of organelle-sized particles between the cell periphery and the bulk can be enhanced by dynamic deformation comparable to that observed in neutrophils. Our results implicate an important mechanism contributing to organelle transport in these motile cells: cytoplasmic flow driven by cell shape deformation

Passive Tracer Dispersion with Random or Periodic Source

In this paper, the author investigates the impact of external sources on the pattern formation and long-time behavior of concentration profiles of passive tracers in a two-dimensional shear flow. It is shown that a time-periodic concentration profile exists for time-periodic external source, while for random source, the distribution functions of all concentration profiles weakly converge to a unique invariant measure (like a stationary state in deterministic systems) as time goes to infinityComment: LaTeX file, 9 page

Periodic orbits of the ABC flow with A=B=C=1A=B=C=1

In this paper, we prove that the ODE system $$\begin{align*} \dot x &=\sin z+\cos y\\ \dot y &= \sin x+\cos z\\ \dot z &=\sin y + \cos x, \end{align*}$$ whose right-hand side is the Arnold-Beltrami-Childress (ABC) flow with parameters $A=B=C=1$, has periodic orbits on $(2\pi\mathbb T)^3$ with rotation vectors parallel to $(1,0,0)$, $(0,1,0)$, and $(0,0,1)$. An application of this result is that the well-known G-equation model for turbulent combustion with this ABC flow on $\mathbb R^3$ has a linear (i.e., maximal possible) flame speed enhancement rate as the amplitude of the flow grows.Comment: 9 page