Shercliff layers in strongly magnetic cylindrical Taylor–Couette flow

Rainer Hollerbach; Deborah Hulot

doi:10.1016/j.crme.2016.02.012

Shercliff layers in strongly magnetic cylindrical Taylor–Couette flow
[Couches de Shercliff dans un écoulement cylindrique fortement magnétique de Taylor–Couette]

Rainer Hollerbach ¹ ; Deborah Hulot ^1,²

¹ Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
² Institut national des sciences appliquées de Rouen, 76801 Saint-Étienne-du-Rouvray cedex, France

Comptes Rendus. Mécanique, Volume 344 (2016) no. 7, pp. 502-509.

Résumé
Abstract

Nous modéliserons l'écoulement axisymétrique de Taylor–Couette en présence d'un champ magnétique axialement périodique, avec un nombre de Hartmann jusqu'à ${Ha}^{2} = 10^{7}$ . La géometrie du champ montre des lignes de champ sous forme de couche de Shercliff. On observe des couches de cisaillement lorsque les frontières sont isolantes, tandis que la rotation est excessive ou inversée pour les frontières conductrices. Certaines configurations de champs sont similaires à celles vues sous forme sphérique ; cependant, de nouvelles configurations existent. Enfin, nous découvrirons l'influence de champs azimutaux ( $B_{ϕ} \sim r^{- 1} {\hat{e}}_{ϕ}$ ) sur ces couches et nous montrerons que l'écoulement diminue avec des bords conducteurs, alors qu'il s'accentue pour des frontières isolantes.

We numerically compute the axisymmetric Taylor–Couette flow in the presence of axially periodic magnetic fields, with Hartmann numbers up to ${Ha}^{2} = 10^{7}$ . The geometry of the field singles out special field lines on which Shercliff layers form. These are simple shear layers for insulating boundaries, versus super-rotating or counter-rotating layers for conducting boundaries. Some field configurations have previously studied spherical analogs, but fundamentally new configurations also exist, having no spherical analogs. Finally, we explore the influence of azimuthal fields $B_{ϕ} \sim r^{- 1} {\hat{e}}_{ϕ}$ on these layers, and show that the flow is suppressed for conducting boundaries, but enhanced for insulating boundaries.

Reçu le : 2015-10-28
Accepté le : 2016-02-29
Publié le : 2016-04-08

DOI : 10.1016/j.crme.2016.02.012

Keywords: Magnetohydrodynamics, Taylor–Couette flow
Mot clés : Magnétohydrodynamique, Écoulement de Taylor–Couette

Affiliations des auteurs :

Rainer Hollerbach ¹ ; Deborah Hulot ^{1, 2}

¹ Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
² Institut national des sciences appliquées de Rouen, 76801 Saint-Étienne-du-Rouvray cedex, France

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     author = {Rainer Hollerbach and Deborah Hulot},
     title = {Shercliff layers in strongly magnetic cylindrical {Taylor{\textendash}Couette} flow},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {502--509},
     publisher = {Elsevier},
     volume = {344},
     number = {7},
     year = {2016},
     doi = {10.1016/j.crme.2016.02.012},
     language = {en},
}

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Rainer Hollerbach; Deborah Hulot. Shercliff layers in strongly magnetic cylindrical Taylor–Couette flow. Comptes Rendus. Mécanique, Volume 344 (2016) no. 7, pp. 502-509. doi : 10.1016/j.crme.2016.02.012. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.02.012/

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