# Steady stokes flow with long-range correlations, fractal fourier spectrum, and anomalous transport.

@article{Zaks2002SteadySF, title={Steady stokes flow with long-range correlations, fractal fourier spectrum, and anomalous transport.}, author={Michael A. Zaks and Arthur V. Straube}, journal={Physical review letters}, year={2002}, volume={89 24}, pages={ 244101 } }

We consider viscous two-dimensional steady flows of incompressible fluids past doubly periodic arrays of solid obstacles. In a class of such flows, the autocorrelations for the Lagrangian observables decay in accordance with the power law, and the Fourier spectrum is neither discrete nor absolutely continuous. We demonstrate that spreading of the droplet of tracers in such flows is anomalously fast. Since the flow is equivalent to the integrable Hamiltonian system with 1 degree of freedom, this…

#### 11 Citations

ANOMALOUS TRANSPORT IN STEADY PLANE FLOWS OF VISCOUS FLUIDS

- Physics
- 2005

We discuss conditions under which Lagrangian observables in time- independent two-dimensional viscous flows have continuous component in the power spectrum, demonstrate decay of correlations and…

Anomalous Transport in Steady Plane Flows of Viscous Fluids

- Physics
- 2005

We discuss conditions under which Lagrangian observables in time-independent two-dimensional viscous flows have continuous component in the power spectrum, demonstrate decay of correlations and…

Anomalous Transport in Steady Plane Viscous Flows: Simple Models

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- 2017

Steady laminar plane flows of incompressible viscous fluids past lattices of solid bodies or arrays of soft obstacles (steady vortices) are less trivial as they may seem to be. Dynamics of tracers in…

Hydrodynamics of fractal continuum flow.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

It is noteworthy to point out that the fractal (quasi)metric defined in this paper implies that the flow of an isotropic fractal continuum obeying the Mandelbrot rule of thumb for intersection is governed by conventional hydrodynamic equations.

Subdiffusive and superdiffusive transport in plane steady viscous flows

- Medicine, PhysicsProceedings of the National Academy of Sciences
- 2018

This work predicts a persistent anomalous dispersion of tracers in time-independent spatially periodic viscous flows, in the absence of either a Lagrangian chaos or a Brownian motion.

Elliptic function representation of doubly periodic two-dimensional Stokes flows

- Physics
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We construct doubly periodic Stokes flows in two dimensions using elliptic functions. This method has advantages when the doubly periodic lattice of obstacles has less than maximal symmetry. We find…

Dynamics at the Border of Chaos and Order

- Physics
- 2003

We give a brief overview of complex dynamical behavior characterized by singular continuous (fractal) Fourier spectra. After presenting a simple example of an aperiodic symbolic sequence we discuss…

Periodic Fundamental Solution of the Two-Dimensional Stokes Equations

- Physics
- 2009

A doubly periodic fundamental solution of the Stokes equations is constructed on the basis of the author's fundamental solution of a Poisson equation recently published in this Journal. It is…

Diffusion effect on passive solute transport inside an infinite two-dimensional array of vortices

- Physics
- 2021

The transport process of solute in a two-dimensional liquid flow is studied. The infinite plane is “covered” by square cells with periodic conditions at its boundaries. The flow is provided by a…

Modelling of Transportation Process in Plane Flows with Stagnation Points

- PhysicsTransport in Porous Media
- 2020

We study transport of passive tracers by plane laminar flows with stagnation points. This setup serves as a simple model of transport in porous media. Close to stagnation points, the flow velocity is…

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