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arXiv · 1310.4543

Selective decay in fluids with advected quantities: MHD and Hall MHD

François Gay-Balmaz·Darryl D. Holm
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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 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 $δ(h+C)=0$. The result holds for Lie-Poisson 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 (MHD).

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François Gay-Balmaz, Darryl D. Holm. 2018-10-20. Selective decay in fluids with advected quantities: MHD and Hall MHD. https://doi.org/10.1088/0951-7715%2F27%2F8%2F1747

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