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Title: Odd surface waves in two-dimensional 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 the linear approximation and study the dispersion of such waves. As expected, the surface waves are chiral and even exist in the absence of gravity and vanishing shear viscosity. In this limit, we derive effective nonlinear Hamiltonian equations for the surface dynamics, generalizing the linear solutions to the weakly nonlinear case. Within the small surface angle approximation, the equation of motion leads to a new class of non-linear chiral dynamics governed by what we dub the chiral Burgers equation. The chiral Burgers equation is identical to the complex Burgers equation with imaginary viscosity and an additional analyticity requirement that enforces chirality. We present several exact solutions of the chiral Burgers equation. For generic multiple pole initial conditions, the system evolves to the formation of singularities in a finite time similar to themore » case of an ideal fluid without odd viscosity. We also obtain a periodic solution to the chiral Burgers corresponding to the non-linear generalization of small amplitude linear waves.« less
Authors:
 [1] ;  [2] ;  [3]
  1. Stony Brook University
  2. The Graduate Center, CUNY
  3. City College of New York, Stony Brook University
Publication Date:
Grant/Contract Number:
DESC-0017662
Type:
Published Article
Journal Name:
SciPost Physics
Additional Journal Information:
Journal Name: SciPost Physics Journal Volume: 5 Journal Issue: 1; Journal ID: ISSN 2542-4653
Publisher:
Stichting SciPost
Sponsoring Org:
USDOE
Country of Publication:
Country unknown/Code not available
Language:
English
OSTI Identifier:
1461900

Abanov, Alexander, Can, Tankut, and Ganeshan, Sriram. Odd surface waves in two-dimensional incompressible fluids. Country unknown/Code not available: N. p., Web. doi:10.21468/SciPostPhys.5.1.010.
Abanov, Alexander, Can, Tankut, & Ganeshan, Sriram. Odd surface waves in two-dimensional incompressible fluids. Country unknown/Code not available. doi:10.21468/SciPostPhys.5.1.010.
Abanov, Alexander, Can, Tankut, and Ganeshan, Sriram. 2018. "Odd surface waves in two-dimensional incompressible fluids". Country unknown/Code not available. doi:10.21468/SciPostPhys.5.1.010.
@article{osti_1461900,
title = {Odd surface waves in two-dimensional incompressible fluids},
author = {Abanov, Alexander and Can, Tankut and Ganeshan, Sriram},
abstractNote = {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 the linear approximation and study the dispersion of such waves. As expected, the surface waves are chiral and even exist in the absence of gravity and vanishing shear viscosity. In this limit, we derive effective nonlinear Hamiltonian equations for the surface dynamics, generalizing the linear solutions to the weakly nonlinear case. Within the small surface angle approximation, the equation of motion leads to a new class of non-linear chiral dynamics governed by what we dub the chiral Burgers equation. The chiral Burgers equation is identical to the complex Burgers equation with imaginary viscosity and an additional analyticity requirement that enforces chirality. We present several exact solutions of the chiral Burgers equation. For generic multiple pole initial conditions, the system evolves to the formation of singularities in a finite time similar to the case of an ideal fluid without odd viscosity. We also obtain a periodic solution to the chiral Burgers corresponding to the non-linear generalization of small amplitude linear waves.},
doi = {10.21468/SciPostPhys.5.1.010},
journal = {SciPost Physics},
number = 1,
volume = 5,
place = {Country unknown/Code not available},
year = {2018},
month = {7}
}