Free surface variational principle for an incompressible fluid with odd viscosity

Abstract

We present variational and Hamiltonian formulations of incompressible fluid dynamics with 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.

arXiv comment9 pages, 1 figure

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• Odd Cosserat elasticity in active materials
• Hydrodynamics of two-dimensional compressible fluid with broken parity: variational principle and free surface dynamics in the absence of dissipation
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• Slip-induced odd viscous flow past a cylinder
• Quantum Hall effective action for anisotropic Dirac semi-metal
• Nonlinear shallow-water waves with vertical odd viscosity