On the dynamics of laminar-turbulent patterns in plane Couette flow

TL;DR

This paper investigates the behavior of laminar-turbulent patterns in plane Couette flow, analyzing how these patterns evolve with changing Reynolds numbers and discussing the implications of their relaxation dynamics.

Contribution

It provides new insights into the relaxation of wavelength modulation in turbulent-laminar patterns and explores the underlying dissipative structures in extended geometries.

Findings

Wavelength modulation relaxes as predicted by dissipative structure theory.

Pattern structuration develops on a turbulent background.

Insights into the transition dynamics between laminar and turbulent regimes.

Abstract

Plane Couette flow presents a regular oblique turbulent-laminar pattern over a wide range of Reynolds numbers R between the globally stable base flow profile at low R<R_g and a uniformly turbulent regime at sufficiently large R>R_t. The numerical simulations that we have performed on a pattern displaying a wavelength modulation show a relaxation of that modulation in agreement with what one would expect from a standard approach in terms of dissipative structures in extended geometry though the structuration develops on a turbulent background. Some consequences are discussed.