On a variational principle for Beltrami flows

In a previous paper [R. González, L. G. Sarasua, and A. Costa, "Kelvin waves with helical Beltrami flow structure," Phys. Fluids20, 024106 (2008)] we analyzed the formation of Kelvin waves with a Beltrami flow structure in an ideal fluid. Here, taking into account the results of this paper...

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Autores principales:	Gonzalez, Rafael, Santini, Eduardo Sergio
Publicado:	2010
Materias:	Arnold's theorem Axisymmetric flow Basic flow Beltrami Beltrami flow Complex topology Eigen-value Enstrophy Euler flows Flow experience Force-free magnetic fields Ideal fluids Kelvin waves Variational principles Eigenvalues and eigenfunctions Flow structure Gravity waves Magnetic fields Magnetohydrodynamics Topology Variational techniques Stability
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10706631_v22_n7_p1_Gonzalez http://hdl.handle.net/20.500.12110/paper_10706631_v22_n7_p1_Gonzalez
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_10706631_v22_n7_p1_Gonzalez
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spelling	paper:paper_10706631_v22_n7_p1_Gonzalez2023-06-08T16:04:32Z On a variational principle for Beltrami flows Gonzalez, Rafael Santini, Eduardo Sergio Arnold's theorem Axisymmetric flow Basic flow Beltrami Beltrami flow Complex topology Eigen-value Enstrophy Euler flows Flow experience Force-free magnetic fields Ideal fluids Kelvin waves Variational principles Eigenvalues and eigenfunctions Flow structure Gravity waves Magnetic fields Magnetohydrodynamics Topology Variational techniques Stability In a previous paper [R. González, L. G. Sarasua, and A. Costa, "Kelvin waves with helical Beltrami flow structure," Phys. Fluids20, 024106 (2008)] we analyzed the formation of Kelvin waves with a Beltrami flow structure in an ideal fluid. Here, taking into account the results of this paper, the topological analogy between the role of the magnetic field in Woltjer's theorem [L. Woltjer, "A theorem on force-free magnetic fields," Proc. Natl. Acad. Sci. U.S.A.44, 489 (1958)] and the role of the vorticity in the equivalent theorem is revisited. Via this analogy we identify the force-free equilibrium of the magnetohydrodynamics with the Beltrami flow equilibrium of the hydrodynamic. The stability of the last one is studied applying Arnold's theorem. We analyze the role of the enstrophy in the determination of the equilibrium and its stability. We show examples where the Beltrami flow equilibrium is stable under perturbations of the Beltrami flow type with the same eigenvalue as the basic flow one. The enstrophy variation results invariant with respect to a uniform rotating and translational frame and the stability is conserved when the flow experiences a transition from a Beltrami axisymmetric flow to a helical one of the same eigenvalue. These results are discussed in comparison with that given by Moffatt in 1986 [H. K. Moffatt, "Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 2. Stability considerations," J. Fluid Mech.166, 359 (1986)]. © 2010 American Institute of Physics. Fil:González, R. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Santini, E.S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2010 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10706631_v22_n7_p1_Gonzalez http://hdl.handle.net/20.500.12110/paper_10706631_v22_n7_p1_Gonzalez
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Arnold's theorem Axisymmetric flow Basic flow Beltrami Beltrami flow Complex topology Eigen-value Enstrophy Euler flows Flow experience Force-free magnetic fields Ideal fluids Kelvin waves Variational principles Eigenvalues and eigenfunctions Flow structure Gravity waves Magnetic fields Magnetohydrodynamics Topology Variational techniques Stability
spellingShingle	Arnold's theorem Axisymmetric flow Basic flow Beltrami Beltrami flow Complex topology Eigen-value Enstrophy Euler flows Flow experience Force-free magnetic fields Ideal fluids Kelvin waves Variational principles Eigenvalues and eigenfunctions Flow structure Gravity waves Magnetic fields Magnetohydrodynamics Topology Variational techniques Stability Gonzalez, Rafael Santini, Eduardo Sergio On a variational principle for Beltrami flows
topic_facet	Arnold's theorem Axisymmetric flow Basic flow Beltrami Beltrami flow Complex topology Eigen-value Enstrophy Euler flows Flow experience Force-free magnetic fields Ideal fluids Kelvin waves Variational principles Eigenvalues and eigenfunctions Flow structure Gravity waves Magnetic fields Magnetohydrodynamics Topology Variational techniques Stability
description	In a previous paper [R. González, L. G. Sarasua, and A. Costa, "Kelvin waves with helical Beltrami flow structure," Phys. Fluids20, 024106 (2008)] we analyzed the formation of Kelvin waves with a Beltrami flow structure in an ideal fluid. Here, taking into account the results of this paper, the topological analogy between the role of the magnetic field in Woltjer's theorem [L. Woltjer, "A theorem on force-free magnetic fields," Proc. Natl. Acad. Sci. U.S.A.44, 489 (1958)] and the role of the vorticity in the equivalent theorem is revisited. Via this analogy we identify the force-free equilibrium of the magnetohydrodynamics with the Beltrami flow equilibrium of the hydrodynamic. The stability of the last one is studied applying Arnold's theorem. We analyze the role of the enstrophy in the determination of the equilibrium and its stability. We show examples where the Beltrami flow equilibrium is stable under perturbations of the Beltrami flow type with the same eigenvalue as the basic flow one. The enstrophy variation results invariant with respect to a uniform rotating and translational frame and the stability is conserved when the flow experiences a transition from a Beltrami axisymmetric flow to a helical one of the same eigenvalue. These results are discussed in comparison with that given by Moffatt in 1986 [H. K. Moffatt, "Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 2. Stability considerations," J. Fluid Mech.166, 359 (1986)]. © 2010 American Institute of Physics.
author	Gonzalez, Rafael Santini, Eduardo Sergio
author_facet	Gonzalez, Rafael Santini, Eduardo Sergio
author_sort	Gonzalez, Rafael
title	On a variational principle for Beltrami flows
title_short	On a variational principle for Beltrami flows
title_full	On a variational principle for Beltrami flows
title_fullStr	On a variational principle for Beltrami flows
title_full_unstemmed	On a variational principle for Beltrami flows
title_sort	on a variational principle for beltrami flows
publishDate	2010
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10706631_v22_n7_p1_Gonzalez http://hdl.handle.net/20.500.12110/paper_10706631_v22_n7_p1_Gonzalez
work_keys_str_mv	AT gonzalezrafael onavariationalprincipleforbeltramiflows AT santinieduardosergio onavariationalprincipleforbeltramiflows
_version_	1768546734616608768

On a variational principle for Beltrami flows

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