Sustaining processes from recurrent flows in body-forced turbulence

TL;DR

This paper investigates the dynamical processes in body-forced turbulence by extracting invariant solutions, revealing the importance of known self-sustaining mechanisms and identifying new transient growth processes in complex flow states.

Contribution

It introduces a method to extract invariant solutions from turbulence data, highlighting the relevance of self-sustaining processes and transient growth mechanisms in body-forced flows.

Findings

Self-sustaining processes are active even in linearly unstable flows.

Multiple mechanisms, including transient growth, explain complex flow states.

Invariant solutions reveal underlying dynamical structures in turbulence.

Abstract

By extracting unstable invariant solutions directly from body-forced three-dimensional turbulence, we study the dynamical processes at play when the forcing is large scale and either unidirectional in the momentum or the vorticity equations. In the former case, the dynamical processes familiar from recent work on linearly-stable shear flows - variously called the Self-Sustaining Process (Waleffe 1997) or Vortex-Wave Interaction (Hall & Smith 1991; Hall & Sherwin 2010) - are important even when the base flow is linearly unstable. In the latter case, where the forcing drives Taylor-Green vortices, a number of mechanisms are observed from the various types of periodic orbits isolated. In particular, two different transient growth mechanisms are discussed to explain the more complex states found.