2019_EJRNL_PP_ALEXANDER_G__ABANOV_11.pdf
Terbatas Ratnasari
» ITB
Terbatas Ratnasari
» ITB
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.