Pattern fluctuations in transitional plane Couette flow

TL;DR

This paper investigates the temporal fluctuations of pattern orientation and wavelength in turbulent-laminar bands of plane Couette flow, modeling their dynamics with a stochastic Landau-type equation.

Contribution

It introduces a novel statistical analysis of pattern fluctuations and proposes a Langevin equation model incorporating turbulence-induced noise.

Findings

Lifetime distributions are exponential.

Pattern orientation and wavelength fluctuate over time.

A Langevin model explains the fluctuation statistics.

Abstract

In wide enough systems, plane Couette flow, the flow established between two parallel plates translating in opposite directions, displays alternatively turbulent and laminar oblique bands in a given range of Reynolds numbers R. We show that in periodic domains that contain a few bands, for given values of R and size, the orientation and the wavelength of this pattern can fluctuate in time. A procedure is defined to detect well-oriented episodes and to determine the statistics of their lifetimes. The latter turn out to be distributed according to exponentially decreasing laws. This statistics is interpreted in terms of an activated process described by a Langevin equation whose deterministic part is a standard Landau model for two interacting complex amplitudes whereas the noise arises from the turbulent background.