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Journal Articles Nonlinearity Year : 2014

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.

Dates and versions

hal-01074223 , version 1 (28-10-2014)

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François Gay-Balmaz, D.D. Holm. A geometric theory of selective decay with applications in MHD. Nonlinearity, 2014, 27 (8), pp.1747-1777. ⟨10.1088/0951-7715/27/8/1747⟩. ⟨hal-01074223⟩
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