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Title:High rayleigh number convection at infinite prandtl number with temperature-dependent viscosity
Author(s):Balachandar, S.; Yuen, David A.; Reuteler, David M.
Subject(s):Temperature Dependent Viscosity
Infinite Prandtl Number
High Rayleigh Number Convection
Abstract:The effects of high Rayleigh number convection for temperature-dependent viscosity at infinite Prandtl number are studied with three-dimensional direct numerical simulations (using a fully spectral method) in a wide box with dimensions 5 X 5 X 1. The form of the temperature-dependent viscosity decreases exponentially with the temperature. Solutions for an volumetrically averaged Rayleigh numbers up to 6.25 X 106 have been obtained for a viscosity contrast of 25. Both models with and without viscous dissipation and adiabatic heatings have been considered. There is a distinct difference in the plume dynamics between models with a dissipation number D=O and D=0.3. At zero dissipation number the hot plumes extend up to the top, while plumes at D=0.3 are cooled due to adiabatic expansion and do not extend throughout the entire layer. The cold descending flows occur in sheets and they form longer wavelength networks and can reach the bottom, regardless of the value of D. At high Rayleigh number there is a transition in the surface toroidal velocity field to a coherent network of river-like structures and compact vortices. Viscous dissipation is found to increase with the Rayleigh number and is particularly strong in regions of downwelling flows. A time- varying depth-dependent mean horizontal flow is produced from the correlation between the laterally varying viscosity field and the velocity gradients.
Issue Date:1994-07
Publisher:Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report:TAM R 761
Genre:Technical Report
Sponsor:National Science Foundation 94/07
Rights Information:Copyright 1994 Board of Trustees of the University of Illinois
Date Available in IDEALS:2021-11-04

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  • Technical Reports - Theoretical and Applied Mechanics (TAM)
    TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.

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