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arXiv · 2304.11421

Monotone energy stability of magnetohydrodynamics Couette and Hartmann flows

Giuseppe Mulone
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Abstract

We study the monotone nonlinear energy stability of \textit{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 Re$_E$ for some selected Prandtl and Hartmann numbers. This result solves a conjecture given in a recent paper by Falsaperla et al. \cite{FMP.2022} and implies a Squire theorem for nonlinear energy: the less stabilizing perturbations in the \textit{energy norm} are the two-dimensional spanwise perturbations. Moreover, for Reynolds numbers less than Re$_E $ there can be no transient energy growth.

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Giuseppe Mulone. 2023-04-22. Monotone energy stability of magnetohydrodynamics Couette and Hartmann flows. https://doi.org/10.1007/s11587-023-00789-7

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