15th European Vacuum Conference (EVC-15)

Variational Principles and Applications of Local Topological Constants of Motion for Non-Barotropic Magnetohydrodynamics

21 Jun 2018, 11:30

20m

Room 4 (CICG)

Contributed Plasma Science & Technology Vacuum Science & Technology

Speaker

Prof. Asher Yahalom (Ariel Univeristy)

Description

Variational principles for magnetohydrodynamics (MHD) were introduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of non-barotropic MHD can be derived for certain field topologies. The variational principle is given in terms of five independent functions for non-stationary non-barotropic flows. This is less than the eight variables which appear in the standard equations of barotropic MHD which are the magnetic field B ⃗ the velocity field v ⃗, the entropy s and the density ρ. The case of non-barotropic MHD in which the internal energy is a function of both entropy and density was not discussed in previous works which were concerned with the simplistic barotropic case. It is important to understand the rule of entropy and temperature for the variational analysis of MHD. Thus we introduce a variational principle of non-barotropic MHD and show that five functions will suffice to describe this physical system.
We will also discuss the implications of the above analysis for topological constants. It will be shown that while cross helicity is not conserved for non-barotropic MHD a variant of this quantity is. The implications of this to non-barotropic MHD stability is discussed.

Bibliography

1. Asher Yahalom “Simplified Variational Principles for non-Barotropic Magnetohydrodynamics”. (arXiv: 1510.00637 [Plasma Physics]) J. Plasma Phys. (2016), vol. 82, 905820204 © Cambridge University Press 2016 doi:10.1017/S0022377816000222.
2. Asher Yahalom “Simplified Variational Principles for Stationary non-Barotropic Magnetohydrodynamics” International Journal of Mechanics, Volume 10, 2016, p. 336-341. ISSN: 1998-4448.
3. 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.