On the MHD boundary of Kelvin-Helmholtz stability diagram at large wavelengths
Autor(a) principal: | |
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Data de Publicação: | 2004 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Brazilian Journal of Physics |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332004000800053 |
Resumo: | 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 (lambda) 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 lambda 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 = 2pid/lambda, 2d is the velocity gradient length scale, and MA is the Alfvénic Mach number) that show both the well-known limit at small lambdas and the boundary for large but finite lambdas 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. |
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Brazilian Journal of Physics |
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On the MHD boundary of Kelvin-Helmholtz stability diagram at large wavelengthsWorking 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 (lambda) 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 lambda 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 = 2pid/lambda, 2d is the velocity gradient length scale, and MA is the Alfvénic Mach number) that show both the well-known limit at small lambdas and the boundary for large but finite lambdas 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.Sociedade Brasileira de Física2004-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332004000800053Brazilian Journal of Physics v.34 n.4b 2004reponame:Brazilian Journal of Physicsinstname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/S0103-97332004000800053info:eu-repo/semantics/openAccessGratton,F. T.Gnavi,G.Farrugia,C. J.Bender,L.eng2005-03-01T00:00:00Zoai:scielo:S0103-97332004000800053Revistahttp://www.sbfisica.org.br/v1/home/index.php/pt/ONGhttps://old.scielo.br/oai/scielo-oai.phpsbfisica@sbfisica.org.br||sbfisica@sbfisica.org.br1678-44480103-9733opendoar:2005-03-01T00:00Brazilian Journal of Physics - Sociedade Brasileira de Física (SBF)false |
dc.title.none.fl_str_mv |
On the MHD boundary of Kelvin-Helmholtz stability diagram at large wavelengths |
title |
On the MHD boundary of Kelvin-Helmholtz stability diagram at large wavelengths |
spellingShingle |
On the MHD boundary of Kelvin-Helmholtz stability diagram at large wavelengths Gratton,F. T. |
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 |
author |
Gratton,F. T. |
author_facet |
Gratton,F. T. Gnavi,G. Farrugia,C. J. Bender,L. |
author_role |
author |
author2 |
Gnavi,G. Farrugia,C. J. Bender,L. |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Gratton,F. T. Gnavi,G. Farrugia,C. J. Bender,L. |
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 (lambda) 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 lambda 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 = 2pid/lambda, 2d is the velocity gradient length scale, and MA is the Alfvénic Mach number) that show both the well-known limit at small lambdas and the boundary for large but finite lambdas 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. |
publishDate |
2004 |
dc.date.none.fl_str_mv |
2004-12-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332004000800053 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332004000800053 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S0103-97332004000800053 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
dc.publisher.none.fl_str_mv |
Sociedade Brasileira de Física |
publisher.none.fl_str_mv |
Sociedade Brasileira de Física |
dc.source.none.fl_str_mv |
Brazilian Journal of Physics v.34 n.4b 2004 reponame:Brazilian Journal of Physics instname:Sociedade Brasileira de Física (SBF) instacron:SBF |
instname_str |
Sociedade Brasileira de Física (SBF) |
instacron_str |
SBF |
institution |
SBF |
reponame_str |
Brazilian Journal of Physics |
collection |
Brazilian Journal of Physics |
repository.name.fl_str_mv |
Brazilian Journal of Physics - Sociedade Brasileira de Física (SBF) |
repository.mail.fl_str_mv |
sbfisica@sbfisica.org.br||sbfisica@sbfisica.org.br |
_version_ |
1754734861866762240 |