Hydrodynamics of two-dimensional compressible fluid with broken parity: Variational principle and free surface dynamics in the absence of dissipation

Alexander G. Abanov, Tankut Can, Sriram Ganeshan, and Gustavo M. Monteiro
Phys. Rev. Fluids 5, 104802 – Published 21 October 2020

Abstract

We consider an isotropic compressible nondissipative fluid with broken parity subject to free surface boundary conditions in two spatial dimensions. The hydrodynamic equations describing the bulk dynamics of the fluid and the free surface boundary conditions depend explicitly on the parity-breaking nondissipative odd viscosity term. We construct an effective action which gives both bulk hydrodynamic equations and free surface boundary conditions. The free surface boundary conditions require an additional boundary term in the action which resembles a 1+1D chiral boson field coupled to the background geometry. We solve the linearized hydrodynamic equations for the deep water case and derive the dispersion of chiral surface waves. We show that in the long-wavelength limit the flow profile exhibits an oscillating vortical boundary layer near the free surface. The layer thickness is controlled by the ratio between the odd viscosity (νo) and the sound velocity (cs), δνo/cs. In the incompressible limit, cs, the vortical boundary layer becomes singular with the vorticity within the layer diverging as ωcs. The boundary layer is formed by odd viscosity coupling the divergence of velocity ·v to vorticity ×v. It results in nontrivial chiral free surface dynamics even in the absence of external forces. The structure of the odd-viscosity-induced boundary layer is very different from the conventional free surface boundary layer associated with dissipative shear viscosity.

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  • Received 20 September 2019
  • Accepted 2 September 2020

DOI:https://doi.org/10.1103/PhysRevFluids.5.104802

©2020 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Alexander G. Abanov1,2, Tankut Can3, Sriram Ganeshan4, and Gustavo M. Monteiro5,6

  • 1Simons Center for Geometry and Physics, Stony Brook, New York 11794, USA
  • 2Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA
  • 3Initiative for the Theoretical Sciences, The Graduate Center, City University of New York, New York, New York 10012, USA
  • 4Department of Physics, City College, City University of New York, New York, New York 10031, USA
  • 5Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas-UNICAMP, 13083-859 Campinas, São Paulo, Brazil
  • 6International Institute of Physics, Campus Universitário Lagoa Nova, 59078-970 Natal, Rio Grande do Norte, Brazil

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Issue

Vol. 5, Iss. 10 — October 2020

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