Anisotropic odd viscosity via a time-modulated drive

Anton Souslov, Andrey Gromov, Vincenzo Vitelli

Research output: Contribution to journalArticlepeer-review

17 Citations (SciVal)
51 Downloads (Pure)


At equilibrium, the structure and response of ordered phases are typically determined by the spontaneous breaking of spatial symmetries. Out of equilibrium, spatial order itself can become a dynamically emergent concept. In this article, we show that spatially anisotropic viscous coefficients and stresses can be designed in a far-from-equilibrium fluid by applying to its constituents a time-modulated drive. If the drive induces a rotation whose rate is slowed down when the constituents point along specific directions, then anisotropic structures and mechanical responses arise at long timescales. We demonstrate that the viscous response of such two-dimensional anisotropic driven fluids can acquire a tensorial, dissipationless component called anisotropic odd (or Hall) viscosity. Classical fluids with internal torques can display additional components of the odd viscosity neglected in previous studies of quantum Hall fluids that assumed angular momentum conservation. We show that, unlike their isotropic counterparts, these anisotropic and angular momentum-violating odd-viscosity coefficients can change even the bulk flow of an incompressible fluid by acting as a source of vorticity. In addition, shear distortions in the shape of an inclusion result in torques. We derive how the odd-viscous coefficients depend on the nonlinear, dissipative response of a fluid of rotating rods, i.e., odd viscosity is not simply given by angular momentum density.

Original languageEnglish
Article number052606
JournalPhysical Review E
Issue number5
Publication statusPublished - 18 May 2020

Bibliographical note

12 pages, 2 figures

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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