Selective decay in fluids with advected quantities: MHD and Hall 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 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 $\delta (h+C)=0$. 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).

As published

References in corpus (3)

• Selective decay by Casimir dissipation in fluids
• Geometric gradient-flow dynamics with singular solutions
• Multiscale Turbulence Models Based on Convected Fluid Microstructure

Cited by in corpus (6)

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• Variational Principles on Geometric Rough Paths and the Lévy Area Correction
• Relaxation to magnetohydrodynamics equilibria via collision brackets
• Exterior dissipation, proportional decay, and integrals of motion
• Structure preserving noise and dissipation in the Toda lattice
• Selective decay for the rotating shallow-water equations with a structure-preserving discretization