Transitions in large eddy simulation of box turbulence

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

A homoclinic tangle on the edge of shear turbulence

Experiments and simulations lend mounting evidence for the edge state hypothesis on subcritical transition to turbulence, which asserts that simple states of fluid motion mediate between laminar and turbulent shear flow as their stable manifolds separate the two in state space. In this Letter we describe a flow homoclinic to a time-periodic edge state. Its existence explains turbulent bursting through the classical Smale-Birkhoff theorem. During a burst, vortical structures and the associated energy dissipation are highly localized near the wall, in contrast to the familiar regeneration cycle