Transitions in large eddy simulation of box turbulence

TL;DR

This paper investigates the transition from laminar to turbulent flow in large eddy simulations of box turbulence, focusing on invariant solutions and flow regimes at different filter scales in a periodic domain.

Contribution

It introduces a LES approach to study turbulence transitions and invariant solutions in a simplified periodic setting, bridging small-scale computations and developed turbulence.

Findings

Transition from laminar to weak turbulence identified

Invariant solutions characterize flow regimes

LES captures flow dynamics at different filter scales

Abstract

One promising decomposition of turbulent dynamics is that into building blocks such as equilibrium and periodic solutions and orbits connecting these. While the numerical approximation of such building blocks is feasible for flows in small domains and at low Reynolds numbers, computations in developed turbulence are currently out of reach because of the large number of degrees of freedom necessary to represent Navier-Stokes flow on all relevant spatial scales. We mitigate this problem by applying large eddy simulation (LES), which aims to model, rather than resolve, motion on scales below the filter length, which is fixed by a model parameter. By considering a periodic spatial domain, we avoid complications that arise in LES modelling in the presence of boundary layers. We consider the motion of an LES fluid subject to a constant body force of the Taylor-Green type as the separation between the forcing length scale and the filter length is increased. In particular, we discuss the transition from laminar to weakly turbulent motion, regulated by simple invariant solution, on a grid of $32^3$ points.