Instability of axially symmetric MHD flows
type: Item
instance of: scholarly article
title: Instability of axially symmetric MHD flows
zbMATH Open document ID: 0861.76030
DOI: 10.1007/BF02078194
author: Yu. G. Gubarev
published in: Fluid Dynamics
publication date: 1997-05-21T00:00:00Z
review text: The problem of linear stability of axially symmetric steady-state flows of an ideal incompressible fluid in a magnetic field is studied. A necessary and sufficient condition for stability of these flows with respect to perturbations of the same symmetry type is obtained by the direct Lyapunov method. This condition represents a generalization of the well-known Rayleigh criterion of ``centrifugal'' stability of rotating streams to the magnetohydrodynamic case. Two-sided exponential estimates of the perturbation growth are derived. A class of the most rapidly growing perturbations is identified, and exact formulas for determining their growth rate are obtained. The corresponding exponents are calculated using the steady flow parameters and initial data for the perturbation field.
Mathematics Subject Classification ID: 76E25
zbMATH DE Number: 939624
zbMATH Keywords: Rayleigh criterion of centrifugal stability
zbMATH Keywords: linear stability
zbMATH Keywords: ideal incompressible fluid
zbMATH Keywords: necessary and sufficient condition of stability
zbMATH Keywords: perturbations
zbMATH Keywords: direct Lyapunov method
MaRDI profile type: Publication
cites work: Q5801898
cites work: Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 2. Stability considerations
cites work: Q3758450
cites work: Q5615994
description: scientific article; zbMATH DE number 939624