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A geometric theory of selective decay with applications in MHD
Abstract : Modifications of the equations of ideal fluid dynamics with advected quantities are introduced that allow selective decay of either the energy h or the Casimir quantities C in the Lie-Poisson (LP) formulation. The dissipated quantity (energy or Casimir, respectively) is shown to decrease in time until the modified system reaches an equilibrium state consistent with ideal energy-Casimir equilibria, namely d(h + C) = 0. The result holds for LP equations in general, independently of the Lie algebra and the choice of Casimir. This selective decay process is illustrated with a number of examples in 2D and 3D magnetohydrodynamics. © 2014 IOP Publishing Ltd & London Mathematical Society.
https://hal-polytechnique.archives-ouvertes.fr/hal-01074223
Contributor : Denis Roura <>
Submitted on : Tuesday, October 28, 2014 - 5:00:02 PM
Last modification on : Wednesday, October 14, 2020 - 4:05:02 AM
Contributor : Denis Roura <>
Submitted on : Tuesday, October 28, 2014 - 5:00:02 PM
Last modification on : Wednesday, October 14, 2020 - 4:05:02 AM
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