The conditions for the non-linear stability of plane and helical mhd flows

V. A. Vladimirov, Yu G. Gubarev

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The stability of the steady flows of an ideal incompressible fluid of uniform density in a magnetic field is investigated. Only those MHD flows are considered which possess one of the types of symmetry (translational, axial, rotational or helical). The sufficient conditions for non-linear stability of the flows in question with respect to perturbations of this symmetry are obtained. These conditions are proved by the method of coupling the integrals of motion [1, 21 in the form [3-81, based on constructing functionals having absolute minima on specified steady solutions. Each of the functionals constructed is the sum of the kinetic energy, the integral of an arbitrary function of the Lagrangian coordinate and another integral, specific for the flows being investigated. The use of Lagrangian ooordinate fields leads to a whole family of new definitions of stability. According to these definitions, deviations of the perturbed flows from the unperturbed ones are measured by the integrals of the squares of the velocity-field and Lagrangiancoordinate perturbations. The stability conditions obtained are extended to existing results [5-7, 9] on new types of flows. These conditions are of an a priori nature since the corresponding theorems of existence of the solutions are not proved.

Original languageEnglish
Pages (from-to)415-423
Number of pages9
JournalJournal of Applied Mathematics and Mechanics
Volume59
Issue number3
DOIs
Publication statusPublished - 1995

Fingerprint

MHD Flow
Nonlinear Stability
Specific integral
Lagrangian Coordinates
Translational symmetry
Perturbation
Integrals of Motion
Ideal Fluid
Steady flow
Magnetohydrodynamics
Steady Flow
Kinetic energy
Stability Condition
Incompressible Fluid
Velocity Field
Deviation
Magnetic Field
Magnetic fields
Symmetry
Fluids

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Applied Mathematics
  • Modelling and Simulation

Cite this

The conditions for the non-linear stability of plane and helical mhd flows. / Vladimirov, V. A.; Gubarev, Yu G.

In: Journal of Applied Mathematics and Mechanics, Vol. 59, No. 3, 1995, p. 415-423.

Research output: Contribution to journalArticle

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