Abstract
In some active systems, such as bacterial suspensions, epithelial tissue monolayers or groups of animals, turbulence-like behaviors have been observed. Particularly in bacterial films, disordered " vortices " with a broad size distribution have been observed, and the structure fluctuates chaotically over time. This phenomenon has been dubbed active turbulence or bacterial turbulence by Raymond E. Goldstein. However, it has nothing to do with classical inertial hydrodynamic turbulence ; the Reynolds number, which measures the importance of inertial effects, is of the order of several thousand in classical inertial turbulence, but for these systems it is extremely small. We are therefore dealing with a new type of low-Reynolds turbulence.
The sixth lecture was devoted to two-dimensional active turbulence for the simplest model of a single-component nematic active gel. A dimensional analysis shows that there is only one dimensionless number measuring the activity, which is proportional to the square of the ratio between the system size and the critical size lcintroduced in the previous lecture. Two models of active turbulence were presented, a mean-field model proposed by Luca Giomi, which considers independent vortices with an exponential size distribution, and a scaling-law model that we proposed with Jaume Casademunt and Ricard Alert, based on numerical simulations for systems with very high activity. These simulations clearly show scaling behavior at very small wave vectors.
