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Free-Surface Variational Principle for an Incompressible Fluid with Odd Viscosity

Alexander G. Abanov and Gustavo M. Monteiro
Phys. Rev. Lett. 122, 154501 – Published 16 April 2019
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Abstract

We present variational and Hamiltonian formulations of incompressible fluid dynamics with a free surface and nonvanishing odd viscosity. We show that within the variational principle the odd viscosity contribution corresponds to geometric boundary terms. These boundary terms modify Zakharov’s Poisson brackets and lead to a new type of boundary dynamics. The modified boundary conditions have a natural geometric interpretation describing an additional pressure at the free surface proportional to the angular velocity of the surface itself. These boundary conditions are believed to be universal since the proposed hydrodynamic action is fully determined by the symmetries of the system.

  • Figure
  • Received 4 December 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.154501

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Alexander G. Abanov

  • Simons Center for Geometry and Physics and Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA

Gustavo M. Monteiro

  • Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas-UNICAMP, 13083-859 Campinas, São Paulo, Brazil

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Issue

Vol. 122, Iss. 15 — 19 April 2019

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