Transition to turbulence in driven active matter

Abstract

A Lorenz-like model was set up recently, to study the hydrodynamic instabilities in a driven active matter system. This Lorenz model differs from the standard one in that all three equations contain non-linear terms. The additional non-linear term comes from the active matter contribution to the stress tensor. In this work, we investigate the non-linear properties of this Lorenz model both analytically and numerically. The significant feature of the model is the passage to chaos through a complete set of period-doubling bifurcations above the Hopf point for inverse Schmidt numbers above a critical value. Interestingly enough, at these Schmidt numbers a strange attractor and stable fixed points coexist beyond the homoclinic point. At the Hopf point, the strange attractor disappears leaving a high-period periodic orbit. This periodic state becomes the expected limit cycle through a set of bifurcations and then undergoes a sequence of period-doubling bifurcations leading to the formation of a strange attractor. This is the first situation where a Lorenz-like model has shown a set of consecutive period-doubling bifurcations in a physically relevant transition to turbulence.arXiv:1908.06247v3 [physics.flu-dyn]

Novel turbulence and coarsening arrest in active-scalar fluids

“…In the inherently nonequilibrium active model H, all terms in the stress tensor do not follow from . In particular, we must include the stress tensor Σ A , which has the form of a nonlinear Burnett term and has the components: 22,24,25,34 where ζ , the activity coefficient,††The activity coefficient is an effective contribution to the stress tensor in eqn (5) and can be written as ζ = σ + ζ ′, where ζ ′ and σ are the active and passive contributions to the stress term in eqn (5). 22 can take both positive and negative values: ζ < 0 ( ζ > 0) for contractile (extensile) swimmers.…”