Spontaneous mirror-symmetry breaking induces inverse energy cascade in 3D active fluids

Classical turbulence theory assumes that energy transport in a 3D turbulent flow proceeds through a Richardson cascade whereby larger vortices successively decay into smaller ones. By contrast, an additional inverse cascade characterized by vortex growth exists in 2D fluids and gases, with profound implications for meteorological flows and fluid mixing. The possibility of a helicity-driven inverse cascade in 3D fluids had been rejected in the 1970s based on equilibrium-thermodynamic arguments. Recently, however, it was proposed that certain symmetry-breaking processes could potentially trigger a 3D inverse cascade, but no physical system exhibiting this phenomenon has been identified to date. Here, we present analytical and numerical evidence for the existence of an inverse energy cascade in an experimentally validated 3D active fluid model, describing microbial suspension flows that spontaneously break mirror symmetry. We show analytically that self-organized scale selection, a generic feature of many biological and engineered nonequilibrium fluids, can generate parity-violating Beltrami flows. Our simulations further demonstrate how active scale selection controls mirror-symmetry breaking and the emergence of a 3D inverse cascade.

Acoustic streaming in two-dimensional freely suspended smectic liquid crystal films

We study horizontal streaming excited by means of a low-frequency and low-intensity acoustic wave in 2D freely suspended films of thermotropic smectic liquid crystals. Acoustic pressure induces fast periodic transverse oscillations of the film, which produce in-plane stationary couples of vortices slowly rotating in opposite directions owing to hydrodynamic nonlinearity. The parameters of the vortices are measured using a new method, based on tracking solidlike disk-shaped islands. The horizontal motion occurs only when the amplitude of the acoustic pressure exceeds the threshold value, which can be explained by Bingham-like behavior of the smectic film. The measurements above threshold are in good agreement with existing theoretical predictions. We demonstrate experimentally that in-plane flow is well controlled by changing the acoustic pressure, excitation frequency, and geometry of the film. The observations open the way to using the phenomenon in nondisplay applications.

Emergent states in dense systems of active rods: from swarming to turbulence

Dense suspensions of self-propelled rod-like particles exhibit a fascinating variety of non-equilibrium phenomena. By means of computer simulations of a minimal model for rigid self-propelled colloidal rods with variable shape we explore the generic diagram of emerging states over a large range of rod densities and aspect ratios. The dynamics is studied using a simple numerical scheme for the overdamped noiseless frictional dynamics of a many-body system in which steric forces are dominant over hydrodynamic ones. The different emergent states are identified by various characteristic correlation functions and suitable order parameter fields. At low density and aspect ratio, a disordered phase with no coherent motion precedes a highly cooperative swarming state with giant number fluctuations at large aspect ratio. Conversely, at high densities weakly anisometric particles show a distinct jamming transition whereas slender particles form dynamic laning patterns. In between there is a large window corresponding to strongly vortical, turbulent flow. The different dynamical states should be verifiable in systems of swimming bacteria and artificial rod-like micro-swimmers.

Meso-scale turbulence in living fluids

Turbulence is ubiquitous, from oceanic currents to small-scale biological and quantum systems. Self-sustained turbulent motion in microbial suspensions presents an intriguing example of collective dynamical behavior among the simplest forms of life and is important for fluid mixing and molecular transport on the microscale. The mathematical characterization of turbulence phenomena in active nonequilibrium fluids proves even more difficult than for conventional liquids or gases. It is not known which features of turbulent phases in living matter are universal or system-specific or which generalizations of the Navier-Stokes equations are able to describe them adequately. Here, we combine experiments, particle simulations, and continuum theory to identify the statistical properties of self-sustained meso-scale turbulence in active systems. To study how dimensionality and boundary conditions affect collective bacterial dynamics, we measured energy spectra and structure functions in dense Bacillus subtilis suspensions in quasi-2D and 3D geometries. Our experimental results for the bacterial flow statistics agree well with predictions from a minimal model for self-propelled rods, suggesting that at high concentrations the collective motion of the bacteria is dominated by short-range interactions. To provide a basis for future theoretical studies, we propose a minimal continuum model for incompressible bacterial flow. A detailed numerical analysis of the 2D case shows that this theory can reproduce many of the experimentally observed features of self-sustained active turbulence.

Universal spectrum of two-dimensional turbulence on a rotating sphere and some basic features of atmospheric circulation on giant planets

The Kolmogorov-Batchelor-Kraichnan (KBK) theory of two-dimensional turbulence is generalized for turbulence on the surface of a rotating sphere. The energy spectrum develops considerable anisotropy; a steep -5 slope emerges in the zonal direction, while in all others the classical KBK scaling prevails. This flow regime in robust steady state is reproduced in simulations with linear drag. The conditions favorable for this regime may be common for giant planets' atmospheric circulations; the same steep spectra are found in their observed zonal velocity profiles and utilized to explain their basic characteristics.