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A note on the stability of Beltrami fields for compressible fluid flows

Affiliation:	1. Department of Physics, University of Zanjan, P.O. Box 45195-313, Zanjan, Iran;2. Department of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran, Iran;1. Laboratory of Magnetism and Magnetic Materials, Advanced Institute of Materials Science, Ton Duc Thang University, Ho Chi Minh City, Viet Nam;2. Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Viet Nam;3. Lehrstuhl für Theoretische Physik I, Technische Universität Dortmund, Otto-Hahn Straße 4, 44221, Dortmund, Germany;1. Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid, Spain;2. Department of Mathematics, Center for Mathematics of the University of Coimbra (CMUC), 3001-454 Coimbra, Portugal;3. Mathematisches Institut, Universität Leipzig, Augustusplatz 10, 04109 Leipzig, Germany

Abstract:	In this paper we study the stability of the magnetostatic equilibrium through a relaxation of a magnetic field B in perfectly conducting compressible and viscous fluid.We establish stability criterion of a large class of Beltrami flows to any admissible displacement about the equilibrium configuration. We show that the field is stable to any displacement with the same 2π-periodicity as the basic flow, except the case where perturbations with wavelength much greater than the scale of the basic flow are included.

Keywords:	Beltrami field Magnetic relaxation Energy principle Instability
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