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}
}
https://doi.org/10.21468/SciPostPhys.5.1.010
Web of Science
Works referenced in this record:
Hydrodynamic Electron Flow and Hall Viscosity
journal, June 2017
- Scaffidi, Thomas; Nandi, Nabhanila; Schmidt, Burkhard
- Physical Review Letters, Vol. 118, Issue 22
Phenomenology of nonrelativistic parity-violating hydrodynamics in 2+1 dimensions
journal, December 2014
- Lucas, Andrew; Surówka, Piotr
- Physical Review E, Vol. 90, Issue 6
Torsional anomalies, Hall viscosity, and bulk-boundary correspondence in topological states
journal, July 2013
- Hughes, Taylor L.; Leigh, Robert G.; Parrikar, Onkar
- Physical Review D, Vol. 88, Issue 2
Nonlinear Hydrodynamics and Fractionally Quantized Solitons at the Fractional Quantum Hall Edge
journal, May 2012
- Wiegmann, P.
- Physical Review Letters, Vol. 108, Issue 20
Hall Viscosity and Electromagnetic Response
journal, February 2012
- Hoyos, Carlos; Son, Dam Thanh
- Physical Review Letters, Vol. 108, Issue 6
Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and paired superfluids
journal, January 2009
- Read, N.
- Physical Review B, Vol. 79, Issue 4
Transport Signatures of the Hall Viscosity
journal, November 2017
- Delacrétaz, Luca V.; Gromov, Andrey
- Physical Review Letters, Vol. 119, Issue 22
The generation of capillary waves by steep gravity waves
journal, May 1963
- Longuet-Higgins, M. S.
- Journal of Fluid Mechanics, Vol. 16, Issue 01
Viscosity of Quantum Hall Fluids
journal, July 1995
- Avron, J. E.; Seiler, R.; Zograf, P. G.
- Physical Review Letters, Vol. 75, Issue 4
Theory of weakly damped free-surface flows: A new formulation based on potential flow solutions
journal, February 2008
- Dias, F.; Dyachenko, A. I.; Zakharov, V. E.
- Physics Letters A, Vol. 372, Issue 8
Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems
journal, April 2012
- Yang, Bo; Papić, Z.; Rezayi, E. H.
- Physical Review B, Vol. 85, Issue 16
Odd viscosity in chiral active fluids
journal, November 2017
- Banerjee, Debarghya; Souslov, Anton; Abanov, Alexander G.
- Nature Communications, Vol. 8, Issue 1
On the ‘wave momentum’ myth
journal, May 1981
- Mcintyre, M. E.
- Journal of Fluid Mechanics, Vol. 106, Issue -1
Swimming at low Reynolds number in fluids with odd, or Hall, viscosity
journal, April 2014
- Lapa, Matthew F.; Hughes, Taylor L.
- Physical Review E, Vol. 89, Issue 4
Hall viscosity, topological states and effective theories
journal, May 2014
- Hoyos, Carlos
- International Journal of Modern Physics B, Vol. 28, Issue 15
Framing Anomaly in the Effective Theory of the Fractional Quantum Hall Effect
journal, January 2015
- Gromov, Andrey; Cho, Gil Young; You, Yizhi
- Physical Review Letters, Vol. 114, Issue 1
Mass Transport in Water Waves
journal, March 1953
- Longuet-Higgins, M. S.
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 245, Issue 903
Geometry of quantum Hall states: Gravitational anomaly and transport coefficients
journal, November 2015
- Can, Tankut; Laskin, Michael; Wiegmann, Paul B.
- Annals of Physics, Vol. 362
Formation of singularities on the free surface of an ideal fluid
journal, February 1994
- Kuznetsov, E. A.; Spector, M. D.; Zakharov, V. E.
- Physical Review E, Vol. 49, Issue 2
Erratum: Lorentz shear modulus of a two-dimensional electron gas at high magnetic field [Phys. Rev. B 76 , 161305(R) (2007)]
journal, May 2009
- Tokatly, I. V.; Vignale, G.
- Physical Review B, Vol. 79, Issue 19
Nonlinear gravity–capillary waves with forcing and dissipation
journal, January 1998
- Fedorov, Alexey V.; Melville, W. Kendall
- Journal of Fluid Mechanics, Vol. 354
Boundary Effective Action for Quantum Hall States
journal, March 2016
- Gromov, Andrey; Jensen, Kristan; Abanov, Alexander G.
- Physical Review Letters, Vol. 116, Issue 12
New Collective Mode in the Fractional Quantum Hall Liquid
journal, January 2007
- Tokatly, I. V.; Vignale, G.
- Physical Review Letters, Vol. 98, Issue 2
Geometric Adiabatic Transport in Quantum Hall States
journal, August 2015
- Klevtsov, S.; Wiegmann, P.
- Physical Review Letters, Vol. 115, Issue 8
Collective field theory for quantum Hall states
journal, December 2015
- Laskin, M.; Can, T.; Wiegmann, P.
- Physical Review B, Vol. 92, Issue 23
Problem of the reversal of a wave for the model equation $$r_t + rr_x - \frac{{ih}}{2}r_{xx} = 0$$
journal, June 1992
- Dobrokhotov, S. Yu.; Maslov, V. P.; Tsvetkov, V. B.
- Mathematical Notes, Vol. 51, Issue 6
Geometrical Description of the Fractional Quantum Hall Effect
journal, September 2011
- Haldane, F. D. M.
- Physical Review Letters, Vol. 107, Issue 11
Fractional Quantum Hall Effect in a Curved Space: Gravitational Anomaly and Electromagnetic Response
journal, July 2014
- Can, T.; Laskin, M.; Wiegmann, P.
- Physical Review Letters, Vol. 113, Issue 4
Odd viscosity in two-dimensional incompressible fluids
journal, September 2017
- Ganeshan, Sriram; Abanov, Alexander G.
- Physical Review Fluids, Vol. 2, Issue 9
Kubo formulas for viscosity: Hall viscosity, Ward identities, and the relation with conductivity
journal, December 2012
- Bradlyn, Barry; Goldstein, Moshe; Read, N.
- Physical Review B, Vol. 86, Issue 24
On the effective hydrodynamics of the fractional quantum Hall effect
journal, June 2013
- Abanov, Alexander G.
- Journal of Physics A: Mathematical and Theoretical, Vol. 46, Issue 29
Quantum Hall Effect and Quillen Metric
journal, November 2016
- Klevtsov, Semyon; Ma, Xiaonan; Marinescu, George
- Communications in Mathematical Physics, Vol. 349, Issue 3
Pole dynamics and oscillations for the complex Burgers equation in the small-dispersion limit
journal, November 1996
- Senouf, D.; Caflisch, R.; Ercolani, N.
- Nonlinearity, Vol. 9, Issue 6
Negative Magnetoresistance in Viscous Flow of Two-Dimensional Electrons
journal, October 2016
- Alekseev, P. S.
- Physical Review Letters, Vol. 117, Issue 16
Anomalous Hydrodynamics of Two-Dimensional Vortex Fluids
journal, July 2014
- Wiegmann, Paul; Abanov, Alexander G.
- Physical Review Letters, Vol. 113, Issue 3
Works referencing / citing this record:
Odd-viscosity-induced stabilization of viscous thin liquid films
journal, September 2019
- Kirkinis, E.; Andreev, A. V.
- Journal of Fluid Mechanics, Vol. 878
The odd free surface flows of a colloidal chiral fluid
journal, September 2019
- Soni, Vishal; Bililign, Ephraim S.; Magkiriadou, Sofia
- Nature Physics, Vol. 15, Issue 11
Topological Waves in Fluids with Odd Viscosity
journal, March 2019
- Souslov, Anton; Dasbiswas, Kinjal; Fruchart, Michel
- Physical Review Letters, Vol. 122, Issue 12
Free-Surface Variational Principle for an Incompressible Fluid with Odd Viscosity
journal, April 2019
- Abanov, Alexander G.; Monteiro, Gustavo M.
- Physical Review Letters, Vol. 122, Issue 15
Dissipative and Hall Viscosity of a Disordered 2D Electron Gas
journal, July 2019
- Burmistrov, Igor S.; Goldstein, Moshe; Kot, Mordecai
- Physical Review Letters, Vol. 123, Issue 2