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This paper investigates the three-dimensional stability of the Lamb–Chaplygin vortex pair. Short-wavelength instabilities, both symmetric and antisymmetric, are found. The antisymmetric mode poss...
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On the onset of convective instabilities in cylindrical cavities heated from below. II. Effect of a magnetic field
The effect of a constant and uniform magnetic field on electrically conducting liquid-metal flow, in cylindrical cavities heated from below, is numerically analyzed by using a spectral element method ...

On the onset of convective instabilities in cylindrical cavities heated from below. I. Pure thermal case

Phys. Fluids 11, 2078 (1999); doi:10.1063/1.870070

Issue Date: August 1999

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R. Touihri, H. Ben Hadid, and D. Henry
Laboratoire de Mécanique des Fluides et d'Acoustique—UMR CNRS 5509, Ecole Centrale de Lyon/ Université Claude Bernard-Lyon 1, ECL, BP 163, 69131 Ecully Cedex, France
Three-dimensional steady flows are simulated in a circular cylindrical cavity of aspect ratio A = H/D, where H is the height and D the diameter of the cavity. The cavity is heated from below and its sidewalls are considered to be adiabatic. The effect of the geometry of the cavity on the onset of convection and on the structure and symmetries of the flow is analyzed. The nonlinear evolution of the convection beyond its onset is presented through bifurcation diagrams for two typical aspect ratios A = 0.5 and A = 1. Axisymmetric (m = 0) and asymmetric (m = 1 and m = 2) azimuthal modes [exp (im phi)] are observed. For A = 0.5, the axisymmetric solution loses its stability to a three-dimensional solution at a secondary bifurcation point. Better understanding of the mechanisms leading to this instability is obtained by analyzing the energy transfer between the basic state and the critical mode. To study the influence of the Prandtl number on the flow pattern and on the secondary bifurcation, three values of the Prandtl number are investigated: Pr=0.02 (liquid metal), Pr=1 (transparent liquids), and Pr=6.7 (water). ©1999 American Institute of Physics.
History: Received 12 August 1998; accepted 30 March 1999
Permalink: http://link.aip.org/link/?PHFLE6/11/2078/1
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EDITORIALLY RELATED

  1. On the onset of convective instabilities in cylindrical cavities heated from below. II. Effect of a magnetic field
    R. Touihri et al.
    Phys. Fluids 11, 2089 (1999)

KEYWORDS and PACS

Keywords
PACS
  • 47.60.+i
    Fluid dynamics Flows in ducts, channels, nozzles, and conduits
  • 47.11.+j
    Fluid dynamics Computational methods in fluid dynamics
  • 47.27.Te
    Fluid dynamics Turbulent flows, convection, and heat transfer Convection and heat transfer
  • 47.52.+j
    Fluid dynamics Chaos
  • 47.20.Ky
    Fluid dynamics Hydrodynamic stability Nonlinearity (including bifurcation theory)
  • YEAR: 1999

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PUBLICATION DATA

ISSN:
1070-6631 (print)   1089-7666 (online)
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