Hamiltonian structure of 2D fluid dynamics with broken parity

Isotropic fluids in two spatial dimensions can break parity symmetry and sustain transverse stresses which do not lead to dissipation. Corresponding transport coefficients include odd viscosity, odd torque, and odd pressure. We consider an isotropic Galilean invariant fluid dynamics in the adiabatic...

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Bibliographic Details
Published in:arXiv.org 2022-12
Main Authors: Monteiro, Gustavo M, Abanov, Alexander G, Ganeshan, Sriram
Format: Article
Language:English
Subjects:
Conservation
Energy dissipation
Fluid dynamics
Fluid flow
Granulation
Hamiltonian functions
Hydrodynamics
Parity
Particle density (concentration)
Transport properties
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Summary:Isotropic fluids in two spatial dimensions can break parity symmetry and sustain transverse stresses which do not lead to dissipation. Corresponding transport coefficients include odd viscosity, odd torque, and odd pressure. We consider an isotropic Galilean invariant fluid dynamics in the adiabatic regime with momentum and particle density conservation. We find conditions on transport coefficients that correspond to dissipationless and separately to Hamiltonian fluid dynamics. The restriction on the transport coefficients will help identify what kind of hydrodynamics can be obtained by coarse-graining a microscopic Hamiltonian system. Interestingly, not all parity-breaking transport coefficients lead to energy conservation and, generally, the fluid dynamics is energy conserving but not Hamiltonian. We show how this dynamics can be realized by imposing a nonholonomic constraint on the Hamiltonian system.
ISSN:2331-8422
DOI:10.48550/arxiv.2105.01655