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.
Abstract. We discuss a minimal generalization of the incompressible Navier-Stokes equations to describe the solvent flow in an active suspension. To account phenomenologically for the presence of an active component driving the ambient fluid flow, we postulate a generic nonlocal extension of the stress-tensor, conceptually similar to those recently introduced in granular media flows. Stability and spectral properties of the resulting hydrodynamic model are studied both analytically and numerically for the two-dimensional (2D) case with periodic boundary conditions. Future generalizations of this momentum-conserving theory could be useful for quantifying the shear properties of active suspensions.
We investigate flow pattern formation and viscosity reduction mechanisms in active fluids by studying a generalized Navier-Stokes model that captures the experimentally observed bulk vortex dynamics in microbial suspensions. We present exact analytical solutions including stress-free vortex lattices and introduce a computational framework that allows the efficient treatment of previously intractable higher-order shear boundary conditions. Large-scale parameter scans identify the conditions for spontaneous flow symmetry breaking, geometry-dependent viscosity reduction and negative-viscosity states amenable to energy harvesting in confined suspensions. The theory uses only generic assumptions about the symmetries and long-wavelength structure of active stress tensors, suggesting that inviscid phases may be achievable in a broad class of non-equilibrium fluids by tuning confinement geometry and pattern scale selection.Self-driven vortical flows in microbial [1] and synthesized active liquids [2-4] often exhibit a dominant length scale [5][6][7][8], distinctly different from the scale-free spectra of conventional turbulence [9]. Experimentally observed vortices in dense bacterial suspensions typically have diameters Λ ∼ 50 − 100 µm [5,8,10] and decay within a few seconds in a bulk fluid [10]. However, when the suspension is enclosed by a small container of dimensions comparable to Λ, individual vortices become stabilized for several minutes [11,12] and can be coupled together to form magnetically ordered vortex lattices [13]. Another form of confinement-induced symmetry breaking was observed recently in a microfluidic realization of bacterial 'racetracks' [14]. For sufficiently narrow tracks of diameter Λ, bacteria spontaneously aligned their swimming directions to form persistent unidirectional currents. These examples illustrate the importance of confinement geometry for flow-pattern formation in non-equilibrium liquids. Conversely, biologically or chemically powered fluids may profoundly affect the dynamics of moving boundaries as active components can significantly alter the effective viscosity of the surrounding solvent fluid [15][16][17]. In particular, recent shear experiments suggest that Escherichia coli bacteria can create effectively inviscid flow if their concentration and activity are sufficiently large to support coherent collective swimming [18]. From a theory perspective, it is desirable to formulate a minimal hydrodynamic model that is analytically tractable and can account for all the aforementioned experimental observations without overfitting.Previous theoretical work [19][20][21][22][23][24] identified potential viscosity reduction mechanisms [15,18] in certain classes of active suspensions, but the complexity and specific nature of the underlying multi-field models have made analytical insight, time-resolved dynamical studies and comparison with experiment challenging. To better understand the general conditions under which active fluids can develop spontaneous symmetry-breaking and quasi-invis...
Recent experiments demonstrate the importance of substrate curvature for actively forced fluid dynamics. Yet, the covariant formulation and analysis of continuum models for nonequilibrium flows on curved surfaces still poses theoretical challenges. Here, we introduce and study a generalized covariant Navier-Stokes model for fluid flows driven by active stresses in nonplanar geometries. The analytical tractability of the theory is demonstrated through exact stationary solutions for the case of a spherical bubble geometry. Direct numerical simulations reveal a curvature-induced transition from a burst phase to an anomalous turbulent phase that differs distinctly from externally forced classical 2D Kolmogorov turbulence. This new type of active turbulence is characterized by the self-assembly of finite-size vortices into linked chains of antiferromagnetic order, which percolate through the entire fluid domain, forming an active dynamic network. The coherent motion of the vortex chain network provides an efficient mechanism for upward energy transfer from smaller to larger scales, presenting an alternative to the conventional energy cascade in classical 2D turbulence.
The ecological interaction between bacteria and sinking particles, such as bacterial degradation of marine snow particles, is regulated by their encounters. Current encounter models focus on the diffusive regime, valid for particles larger than the bacterial run length, yet the majority of marine snow particles are small, and the encounter process is then ballistic. Here, we analytically and numerically quantify the encounter rate between sinking particles and non-motile or motile microorganisms in the ballistic regime, explicitly accounting for the hydrodynamic shear created by the particle and its coupling with micro-organism shape. We complement results with selected experiments on non-motile diatoms. The shape-shear coupling has a considerable effect on the encounter rate and encounter location through the mechanisms of hydrodynamic focusing and screening, whereby elongated micro-organisms preferentially orient normally to the particle surface downstream of the particle (focusing) and tangentially to the surface upstream of the particle (screening). Non-motile elongated micro-organisms are screened from sinking particles because shear aligns them tangentially to the particle surface, which reduces the encounter rate by a factor proportional to the square of the micro-organism aspect ratio. For motile elongated micro-organisms, hydrodynamic focusing increases the encounter rate when particle sinking speed is similar to microorganism swimming speed, whereas for very quickly sinking particles hydrodynamic screening can reduce the encounter rate below that of non-motile micro-organisms. For natural ocean conditions, we connect the ballistic and diffusive limits and compute the encounter rate as a function of shape, motility and particle characteristics. Our results indicate that shear should be taken into account to predict the interactions between bacteria and sinking particles responsible for the large carbon flux in the ocean's biological pump.
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