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New class of turbulence in active fluids

  1. Erwin Freyc
  1. aTokamak Physics Division, Max Planck Institute for Plasma Physics, D-85748 Garching, Germany;
  2. bDepartment of Physics and Astronomy, University of California, Los Angeles, CA 90095;
  3. cArnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, D-80333 Munich, Germany

  1. Edited by Alexander J. Smits, Princeton University, Princeton, NJ, and accepted by the Editorial Board October 29, 2015 (received for review May 12, 2015)

Significance

It is widely appreciated that turbulence is one of the main challenges of modern theoretical physics. Whereas up to now, most work in this area has been dedicated to the study of Navier–Stokes flows, numerous examples exist of systems that exhibit similar types of spatiotemporal chaos but are described by more complex nonlinear equations. One such problem of quickly growing scientific interest is turbulence in active fluids. We find that such systems can exhibit power-law energy spectra with nonuniversal exponents as a result of nonlinear self-organization, defining a new class of turbulent flows.

Abstract

Turbulence is a fundamental and ubiquitous phenomenon in nature, occurring from astrophysical to biophysical scales. At the same time, it is widely recognized as one of the key unsolved problems in modern physics, representing a paradigmatic example of nonlinear dynamics far from thermodynamic equilibrium. Whereas in the past, most theoretical work in this area has been devoted to Navier–Stokes flows, there is now a growing awareness of the need to extend the research focus to systems with more general patterns of energy injection and dissipation. These include various types of complex fluids and plasmas, as well as active systems consisting of self-propelled particles, like dense bacterial suspensions. Recently, a continuum model has been proposed for such “living fluids” that is based on the Navier–Stokes equations, but extends them to include some of the most general terms admitted by the symmetry of the problem [Wensink HH, et al. (2012) Proc Natl Acad Sci USA 109:14308–14313]. This introduces a cubic nonlinearity, related to the Toner–Tu theory of flocking, which can interact with the quadratic Navier–Stokes nonlinearity. We show that as a result of the subtle interaction between these two terms, the energy spectra at large spatial scales exhibit power laws that are not universal, but depend on both finite-size effects and physical parameters. Our combined numerical and analytical analysis reveals the origin of this effect and even provides a way to understand it quantitatively. Turbulence in active fluids, characterized by this kind of nonlinear self-organization, defines a new class of turbulent flows.

Footnotes

  • ↵1To whom correspondence should be addressed. Email: jenko{at}physics.ucla.edu.

  • Author contributions: F.J. designed research; V.B., F.J., and E.F. performed research; and V.B., F.J., and E.F. wrote the paper.

  • The authors declare no conflict of interest.

  • This article is a PNAS Direct Submission. A.J.S. is a guest editor invited by the Editorial Board.

  • This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1509304112/-/DCSupplemental.

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