The concept of label symmetries is related through the Noether theorem to the important conservation laws of ideal fluid dynamics. Among those are local conservations laws of potential vorticities and global conservation laws of circulation in barotropic flows. Subgroups of the labelling group are connected to topological conservation laws. For example it was shown that the Metage symmetry group is connected to the conservation of Helicity in barotropic flows and the conservation of cross helicity in barotropic magnetohydrodynamics. In both cases the choice of the labels is restricted by attaching them to comoving physical lines. Those are vortex lines for the fluid dynamical case and magnetic lines for the magnetohydrodynamic case. It should be remarked that recently a way was found to expand the realm of Metage symmetries also to non-barotropic magnetohydrodynamics and thus obtain a generalization of the cross helicity conservation law for this case. This new topological constant of motion was also found using non-single valued variational variables. Topological conservations laws seem to play an important rule also in quantum spin fluid dynamics. In this talk we will review some of the results associated with label symmetry sub groups and the associated conservation laws.

References

1. Asher Yahalom “Non-Barotropic Cross-helicity Conservation Applications in Magnetohydrodynamics and the Aharanov - Bohm effect" (arXiv:1703.08072 [physics.plasm-ph]). Fluid Dynamics Research, Volume 50, Number 1, 011406. https://doi.org/10.1088/1873-7005/aa6fc7 . Received 11 December 2016, Accepted Manuscript online 27 April 2017, Published 30 November 2017.
2. Yahalom A. (2018) Metage Symmetry Group of Non-barotropic Magnetohydrodynamics and the Conservation of Cross Helicity. In: Dobrev V. (eds) Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 2. LT-XII/QTS-X 2017. Springer Proceedings in Mathematics & Statistics, vol 255. Springer Nature, Singapore (arXiv:1801.06443 [physics.plasm-ph]).