On the MHD boundary of Kelvin-Helmholtz stability diagram at large wavelengths

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Working within the domain of inviscid incompressible MHD theory, we found that a tangential discontinuity (TD) separating two uniform regions of different density, velocity and magnetic field may be Kelvin-Helmholtz (KH) stable and yet a study of a transition between the same constant regions given...

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Autores principales: Gratton, F.T., Gnavi, G., Farrugia, C.J., Bender, L.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2004
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_01039733_v34_n4B_p1804_Gratton
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paperaa:paper_01039733_v34_n4B_p1804_Gratton2023-06-12T16:46:30Z On the MHD boundary of Kelvin-Helmholtz stability diagram at large wavelengths Braz. J. Phys. 2004;34(4 B):1804-1813 Gratton, F.T. Gnavi, G. Farrugia, C.J. Bender, L. Working within the domain of inviscid incompressible MHD theory, we found that a tangential discontinuity (TD) separating two uniform regions of different density, velocity and magnetic field may be Kelvin-Helmholtz (KH) stable and yet a study of a transition between the same constant regions given by a continuous velocity profile shows the presence of the instability with significant growth rates. Since the cause of the instability stems from the velocity gradient, and since a TD may be considered as the ultimate limit of such gradient, the statement comes as a surprise. In fact, a long wavelength (λ) boundary for the KH instability does not exist in ordinary liquids being instead a consequence of the presence of magnetic shear, a possibility that has passed unnoticed in the literature. It is shown that KH modes of a magnetic field configuration with constant direction do not have the long A boundary. A theoretical explanation of this feature and examples of the violation of the TD stability condition are given using a model that can be solved in closed form. Stability diagrams in the (kd, MA) plane are given (where kd = 2πd/λ, 2d is the velocity gradient length scale, and MA is the Alfvénic Mach number) that show both the well-known limit at small λs and the boundary for large but finite As noted here. Consequences of this issue are relevant for stability studies of the dayside magnetopause as the stability condition for a TD should be used with care in data analysis work. Fil:Gratton, F.T. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Gnavi, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Bender, L. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2004 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_01039733_v34_n4B_p1804_Gratton
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
description Working within the domain of inviscid incompressible MHD theory, we found that a tangential discontinuity (TD) separating two uniform regions of different density, velocity and magnetic field may be Kelvin-Helmholtz (KH) stable and yet a study of a transition between the same constant regions given by a continuous velocity profile shows the presence of the instability with significant growth rates. Since the cause of the instability stems from the velocity gradient, and since a TD may be considered as the ultimate limit of such gradient, the statement comes as a surprise. In fact, a long wavelength (λ) boundary for the KH instability does not exist in ordinary liquids being instead a consequence of the presence of magnetic shear, a possibility that has passed unnoticed in the literature. It is shown that KH modes of a magnetic field configuration with constant direction do not have the long A boundary. A theoretical explanation of this feature and examples of the violation of the TD stability condition are given using a model that can be solved in closed form. Stability diagrams in the (kd, MA) plane are given (where kd = 2πd/λ, 2d is the velocity gradient length scale, and MA is the Alfvénic Mach number) that show both the well-known limit at small λs and the boundary for large but finite As noted here. Consequences of this issue are relevant for stability studies of the dayside magnetopause as the stability condition for a TD should be used with care in data analysis work.
format Artículo
Artículo
publishedVersion
author Gratton, F.T.
Gnavi, G.
Farrugia, C.J.
Bender, L.
spellingShingle Gratton, F.T.
Gnavi, G.
Farrugia, C.J.
Bender, L.
On the MHD boundary of Kelvin-Helmholtz stability diagram at large wavelengths
author_facet Gratton, F.T.
Gnavi, G.
Farrugia, C.J.
Bender, L.
author_sort Gratton, F.T.
title On the MHD boundary of Kelvin-Helmholtz stability diagram at large wavelengths
title_short On the MHD boundary of Kelvin-Helmholtz stability diagram at large wavelengths
title_full On the MHD boundary of Kelvin-Helmholtz stability diagram at large wavelengths
title_fullStr On the MHD boundary of Kelvin-Helmholtz stability diagram at large wavelengths
title_full_unstemmed On the MHD boundary of Kelvin-Helmholtz stability diagram at large wavelengths
title_sort on the mhd boundary of kelvin-helmholtz stability diagram at large wavelengths
publishDate 2004
url http://hdl.handle.net/20.500.12110/paper_01039733_v34_n4B_p1804_Gratton
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AT gnavig onthemhdboundaryofkelvinhelmholtzstabilitydiagramatlargewavelengths
AT farrugiacj onthemhdboundaryofkelvinhelmholtzstabilitydiagramatlargewavelengths
AT benderl onthemhdboundaryofkelvinhelmholtzstabilitydiagramatlargewavelengths
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