Abstract
A rigorous approach by E.M. Barston (1977) 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-dumbbell' theorem is established which is considerably stronger than the semicircle theorem. Possible astrophysical applications are discussed.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
