Transport Scaling Laws in Turbulent Active Fluids
ABSTRACT :
Turbulence is ubiquitous in nature and is observed at different length scale ranging from a stirred cup of coffee to astrophysical systems such as galactic interiors. As turbulent state is an ensemble of highly irregular and non-linear processes rendering it amenable only through statistical methods. A large body of work already exists in area of passive turbulence in high temperature plasmas in Tokomaks, stellar magnetohydrodynamics, oceans and atmospheric systems, to mention a few. Inspite of the volume of work done, turbulence is still considered by many as the last unresolved problem of classical physics meaning that there is a general lack of predictability in physical properties such as steady state transport with respect to varying initial conditions. In this study we turn our attention to systems having more general form of energy injection, transfer and dissipation, in particular dense bacterial suspensions which are of tremendous interest to the community of bio-physicists. By using a continuum model that well describes dense bacterial suspensions, we study the role of friction (and energy injection) in the transport of tracer particles that go with the local flow. We predict a new scaling law for mean square velocity in these system which together with the known scaling laws for energy spectrum at low wave-numbers allows us to predict scaling laws for both the Diffusion coefficient D and crossover time Ï„ c from ballistic to diffusive regime. Using our scaling laws we are also able to explain why Ï„ c develops a minimum at zero friction thereby implying that the fastest relaxation of tracers happens when friction is absent.