Odd surface waves in two-dimensional incompressible fluids
Abstract
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 »
- Authors:
-
- Stony Brook University
- The Graduate Center, CUNY
- City College of New York, Stony Brook University
- Publication Date:
- Research Org.:
- State Univ. of New York (SUNY), Albany, NY (United States); Stony Brook Univ., NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
- OSTI Identifier:
- 1461900
- Alternate Identifier(s):
- OSTI ID: 1596115; OSTI ID: 1805206
- Grant/Contract Number:
- SC0017662
- Resource Type:
- Published Article
- Journal Name:
- SciPost Physics Proceedings
- Additional Journal Information:
- Journal Name: SciPost Physics Proceedings Journal Volume: 5 Journal Issue: 1; Journal ID: ISSN 2542-4653
- Publisher:
- SciPost Foundation
- Country of Publication:
- Netherlands
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Burgers equation; Hydrodynamics; Incompressible fluids; Parity symmetry; Shear viscosity; Viscosity
Citation Formats
Abanov, Alexander, Can, Tankut, and Ganeshan, Sriram. Odd surface waves in two-dimensional incompressible fluids. Netherlands: N. p., 2018.
Web. doi:10.21468/SciPostPhys.5.1.010.
Abanov, Alexander, Can, Tankut, & Ganeshan, Sriram. Odd surface waves in two-dimensional incompressible fluids. Netherlands. https://doi.org/10.21468/SciPostPhys.5.1.010
Abanov, Alexander, Can, Tankut, and Ganeshan, Sriram. Fri .
"Odd surface waves in two-dimensional incompressible fluids". Netherlands. https://doi.org/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 Proceedings},
number = 1,
volume = 5,
place = {Netherlands},
year = {2018},
month = {7}
}
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https://doi.org/10.21468/SciPostPhys.5.1.010
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Cited by: 34 works
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Works referencing / citing this record:
Odd-viscosity-induced stabilization of viscous thin liquid films
journal, September 2019
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- Journal of Fluid Mechanics, Vol. 878
The odd free surface flows of a colloidal chiral fluid
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Topological Waves in Fluids with Odd Viscosity
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Free-Surface Variational Principle for an Incompressible Fluid with Odd Viscosity
journal, April 2019
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Dissipative and Hall Viscosity of a Disordered 2D Electron Gas
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