Eigenvalue bounds in magnetoatmospheric shear flow

Details Eigenvalue bounds in magnetoatmospheric shear flow Eigenvalue bounds in magnetoatmospheric shear flow

Oct 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980jpha...13.3325a&link_type=abstract

Journal of Physics A - Mathematical and General, vol. 13, Oct. 1980, p. 3325-3338.

Astronomy and Astrophysics

Astrophysics

6

Atmospheric Circulation, Boundary Value Problems, Eigenvalues, Geomagnetism, Incompressible Fluids, Magnetohydrodynamic Stability, Shear Flow, Astrophysics, Atmospheric Stratification, Differential Equations, Magnetohydrodynamic Flow, Parallel Flow, Stellar Atmospheres

Scientific paper

A rigorous approach by Barston to stability of Lagrangian systems is used to establish both rectangle and semicircle theorems for plane parallel flow along a horizontal but otherwise arbitrary magnetic field, permeating a perfectly electrically conducting incompressible fluid under gravity. The radius of the semicircle is reduced by magnetic effects and stable stratification. A Richardson criterion for stability against constant shear flow is also derived. The analogous problem for a compressible fluid is also discussed, and for a certain class of disturbances a 'semi-dumbell' theorem is established which is considerably stronger than the semicircle theorem. Possible astrophysical applications are discussed.

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