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

Abstract

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.

Linearly forced fluid flow on a rotating sphere

“…Conceptually, our analysis supports the view that non-equilibrium approaches can provide analytical insights into the dynamics of planetary flows (Delplace et al 2017) and atmospheres (Marston 2011(Marston , 2012. Moreover, in view of the recent successful application of phenomenological GNS models to active fluids (Dunkel et al 2013;S lomka & Dunkel 2017b), the results of this study can also help advance the understanding of active matter propagation on curved surfaces (Sanchez et al 2012;Sknepnek & Henkes 2015;Zhang et al 2016;Henkes et al 2018;Nitschke et al 2019) and in rotating frames (Löwen 2019).…”

“…Unstable bands are a universal feature of stress tensors exhibiting positive dispersion ζ(k) > 0 for some k. Polynomial GNS models of the type (2.1) were first studied in the context of seismic wave propagation (Beresnev & Nikolaevskiy 1993;Tribelsky & Tsuboi 1996) and can also capture essential statistical properties of dense microbial suspensions (Dunkel et al 2013;S lomka & Dunkel 2017b). Since non-polynomial dispersion relation produce qualitatively similar flows Linkmann et al 2019), we focus here on stress tensors of the generic polynomial form (2.1c).…”

“…Theoretical and computational studies of turbulence phenomena typically focus on external driving provided by a random forcing (Boffetta & Ecke 2012), boundary forcing (Grossmann et al 2016) or Kolmogorov forcing (Lucas & Kerswell 2014). A fundamentally different class of internal driving mechanisms, less widely explored in the turbulence literature so far, is based on linear instabilities (Rothman 1989;Tribelsky & Tsuboi 1996;S lomka & Dunkel 2017b;Linkmann et al 2019). The profound mathematical differences between external and internal driving were emphasized by Arnold (1991) in the context of classical dynamical systems described by ordinary differential equations.…”

“…To gain insight into this problem, we investigate an analytically tractable minimal model for linearly forced quasi-2D flow on a rotating sphere. The underlying generalized Navier-Stokes (GNS) equations describe internally driven flows through higher-order hyperviscosity-like terms in the stress tensor (Beresnev & Nikolaevskiy 1993;S lomka & Dunkel 2017b), and the associated GNS triad dynamics is structurally similar to the Lorenz system (S lomka et al 2018). GNS-type models have been studied previously as effective phenomenological descriptions for seismic wave propagation (Beresnev & Nikolaevskiy 1993;Tribelsky & Tsuboi 1996), magnetohydrodynamic flows (Vasil 2015) and active fluids (S lomka & Dunkel 2017b,a;James et al 2018).…”

Helicity Dynamics, Inverse, and Bidirectional Cascades in Fluid and Magnetohydrodynamic Turbulence: A Brief Review

“…Recently, it was also shown in Somka and Dunkel () that, in the context of bacterial suspensions and using the Navier‐Stokes equations for the solvent with a stress tensor including higher‐order terms modeling the role of the non‐Newtonian active part of the fluid, an accumulation of energy at large scales occurred because of an instability due to the bi‐Laplacian forcing. One peculiar feature of these solutions is that they can be fully helical, Beltrami flows, ω = λ v , by selecting the scales for which the three linear terms (proportional in Fourier space to k 2 n , n = 1,2,3) can balance each other exactly.…”