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A bstract We show that barotropic flows of a perfect, charged, classical fluid exhibit an anomaly analogous to the chiral anomaly known in quantum field theories with Dirac fermions. A prominent effect of the chiral anomaly is the transport electric current in the fluid at equilibrium with the chiral reservoir. We find that it is also a property of celebrated Beltrami flows — stationary solutions of the Euler equation with an extensive helicity.
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Anomalies in fluid dynamics: flows in a chiral background via variational principle
Abstract We study flows of barotropic perfect fluid under the simultaneous action of the electromagnetic field and the axial–vector potential, the external field conjugate to the fluid helicity. We obtain the deformation of the Euler equation by the axial–vector potential and the deformations of various currents by two external fields. We show that the divergence of the vector and axial currents are controlled by the chiral anomaly known in quantum field theories with Dirac fermions. We obtain these results by extending the variational principle for barotropic flows of a perfect fluid by coupling with the external axial–vector potential.
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- Award ID(s):
- 2116767
- PAR ID:
- 10378904
- Date Published:
- Journal Name:
- Journal of Physics A: Mathematical and Theoretical
- Volume:
- 55
- Issue:
- 41
- ISSN:
- 1751-8113
- Page Range / eLocation ID:
- 414001
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1088/1751-8121/ac9202
