Particles and Fields in Active Turbulence

Abstract

I have extended various facets of modern turbulence theory to hydrodynamic models of dense bacterial suspensions, which show turbule= nt-like patterns, dubbed active turbulence. By using direct numerical simulations (DNSs) and methods of analysis, we address issues of irreversibility, intermittency, and regularity for two models of active turbulence. Our results uncover intriguing similarities ( and differences) between high-Reynolds-number incompressible fluid turbulence and low-Reynolds-number active turbulence. Specifically, we investigate the following problems:

1. Irreversibility in bacterial turbulence: Insights from the mean-bacterial-velocity model. We show how signatures of irreversibility in bacterial or active turbulence are markedly different from those in high-Reynolds-number inertial turbulence. 2. Eulerian and Lagrangian Intermittency in Active Turbulence: We show, by using a hydrodynamical model, the onset of intermittency, and the consequent multiscaling of Eulerian and Lagrangian structure functions, as a function of the activity. 3. Attractor dimension for a model of active turbulence: We obtain numerical estimates of the attractor dimension of a hydrodynamical PDE that has been proposed to understand bacterial turbulence; we then compare the results with analytical estimates. 4. An analytical and computational study of the incompressible Toner–Tu equations: We show global regularity for a continuum model of flocking in two dimensions. Furthermore, via DNS, we show how activity distinguishes weak solutions of incompressible Toner-Tu equations from their counterparts for the Navier-Stokes equations. 5. Turbulent cascade arrests and the formation of intermediate-scale condensates: We demonstrate, by using shell models, an energy-transfer mechanism for turbulence stemming from odd-viscosity-type models.