Free surface variational principle for an incompressible fluid with odd viscosity

TL;DR

This paper develops a variational and Hamiltonian framework for incompressible fluids with free surfaces and odd viscosity, revealing boundary effects and geometric interpretations that modify classical dynamics.

Contribution

It introduces a novel variational principle incorporating odd viscosity as boundary terms, leading to new boundary conditions and dynamics in fluid systems.

Findings

Boundary terms correspond to odd viscosity effects

Modified boundary conditions relate to surface angular velocity

Hydrodynamic action determined by system symmetries

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.