Monotone energy stability of magnetohydrodynamics Couette and Hartmann flows
Abstract
We study the monotone nonlinear energy stability of magnetohydrodynamics plane shear flows, Couette and Hartmann flows. We prove that the least stabilizing perturbations, in the energy norm, are the two-dimensional spanwise perturbations and give some criti\-cal Reynolds numbers ReE for some selected Prandtl and Hartmann numbers. This result solves a conjecture given in a recent paper by Falsaperla et al. FMP.2022 and implies a Squire theorem for nonlinear energy: the less stabilizing perturbations in the energy norm are the two-dimensional spanwise perturbations. Moreover, for Reynolds numbers less than ReE there can be no transient energy growth.
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