On the decay of turbulence in plane Couette flow

TL;DR

This paper investigates how turbulence decays in plane Couette flow by using direct numerical simulations, revealing a two-stage process involving band rupture and slow regression, and reinterpreting decay through a spatiotemporal stochastic framework.

Contribution

It introduces a spatiotemporal perspective on turbulence decay in plane Couette flow and demonstrates a two-stage decay process using large deviations theory.

Findings

Decay involves band rupture and slow regression.

Large deviations provide a new interpretation of decay.

Simulations confirm the two-stage decay process.

Abstract

The decay of turbulent and laminar oblique bands in the lower transitional range of plane Couette flow is studied by means of direct numerical simulations of the Navier--Stokes equations. We consider systems that are extended enough for several bands to exist, thanks to mild wall-normal under-resolution considered as a consistent and well-validated modelling strategy. We point out a two-stage process involving the rupture of a band followed by a slow regression of the fragments left. Previous approaches to turbulence decay in wall-bounded flows making use of the chaotic transient paradigm are reinterpreted within a spatiotemporal perspective in terms of large deviations of an underlying stochastic process.