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

Author(s)

Abanov, Alexander G. ^{[1, 2]} ; Monteiro, Gustavo M. ^[3]

Affiliation

^[1] SUNY Stony Brook, Dept Phys & Astron, Stony Brook, NY 11794 - USA

^[2] SUNY Stony Brook, Simons Ctr Geometry & Phys, Stony Brook, NY 11794 - USA

^[3] Univ Estadual Campinas, Inst Fis Gleb Wataghin, UNICAMP, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: Physical Review Letters; v. 122, n. 15 APR 16 2019.
• Web of Science Citations: 0

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. (AU)

• FAPESP's process: 16/13517-0 - Topological and transport properties of chiral materials
• Grantee: Gustavo Machado Monteiro
• Support Opportunities: Scholarships in Brazil - Post-Doctoral