Odd surface waves in 2+1D incompressible fluids.
We consider free surface dynamics of a two-dimensional incompressible fluid with odd viscosity. The odd viscosity is a peculiar part of the viscosity tensor which does not result in dissipation and is allowed when parity symmetry is broken. For the case of incompressible fluids, the odd viscosity manifests itself through the free surface (no stress) boundary conditions. We first find the free surface wave solutions of hydrodynamics in linear approximations and study the dispersion of such waves. As expected, the surface waves are chiral. It turns out that due to odd viscosity and in the limit of vanishing shear viscosity, the propagating chiral wave solutions exist even in the absence of gravity. We derive an effective nonlinear equation for surface dynamics generalizing the obtained linear solutions to the weakly nonlinear case. This equation is equivalent to the complex Burgers equation with an additional analyticity requirement. This equation possesses multiple pole solutions at least for a finite time.
Publisher URL: http://arxiv.org/abs/1801.10150
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