Steady Stokes flow with long-range correlations, fractal Fourier spectrum, and anomalous transport

TL;DR

This paper studies steady two-dimensional viscous flows with complex spectral properties and long-range correlations, revealing anomalous transport behavior linked to integrable Hamiltonian dynamics.

Contribution

It demonstrates that certain steady flows exhibit long-range correlations, fractal Fourier spectra, and anomalous transport, connecting these phenomena to integrable Hamiltonian systems.

Findings

Autocorrelations decay as a power law.

Fourier spectrum is fractal, neither discrete nor continuous.

Droplet spreading is anomalously fast.

Abstract

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 provides an example of integrable dynamics with long-range correlations, fractal power spectrum, and anomalous transport properties.