A note on Bödewadt-Hartmann layers

P. A. Davidson, A. Pothérat

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)

Abstract

This paper addresses the problem of axisymetric rotating flows bounded by a fixed horizontal plate and subject to a permanent, uniform, vertical magnetic field (the so-called Bödewadt-Hartmann problem). The aim is to find out which one of the Coriolis or the Lorentz force dominates the dynamics (and hence the boundary layer thickness) when their ratio, represented by the Elsasser number A, varies. After a short review of existing linear solutions of the semi infinite Ekman-Hartmann problem, weakly non-linear analytical solutions as well as fully non-linear numerical solutions are given. The case of a rotating vortex in a finite depth fluid layer is then studied, first when the flow is steady under a forced rotation and second for spin-down from some initial state. The angular velocity in the first case and decay time in the second are obtained analytically as a function of A using the weakly non linear results of the semi-infinite Bödewadt-Hartmann problem.

Original languageEnglish
Pages (from-to)545-559
Number of pages15
JournalEuropean Journal of Mechanics, B/Fluids
Volume21
Issue number5
Early online date12 Oct 2002
DOIs
Publication statusPublished - 13 Oct 2002
Externally publishedYes

Keywords

  • Axisymetric flows
  • Ekman-Bödewadt layers
  • Hartmann
  • Kàrman approximation
  • MHD
  • Rotating flows

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)

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