A boundary-layer analysis of Benard convection in a fluid of strongly temperature-dependent viscosity

Details A boundary-layer analysis of Benard convection in a fluid of strongly temperature-dependent viscosity A boundary-layer analysis of Benard convection in a fluid of strongly temperature-dependent viscosity

Dec 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984pepi...36..355m&link_type=abstract

(International Association of Seismology and Physics of the Earth's Interior, Symposium on Quantitative Geodynamics Lithospheric

Physics

69

Benard Cells, Boundary Layer Flow, Geophysical Fluids, Planetary Evolution, Rheology, Temperature Dependence, Viscous Fluids, Asymptotic Methods, Boundary Value Problems, Boussinesq Approximation, Prandtl Number, Rayleigh Number, Reynolds Number, Two Dimensional Flow

Scientific paper

A theory of Benard convection is given for a fluid whose viscosity depends strongly on temperature, so that the essential viscosity variations in a given thermal boundary layer occur in a sublayer very thin compared to the thermal layer containing it. This separation of length scales is used to develop a specific theory for a flow in which the essential viscosity variations are associated with a cold surface rather than a hot one. The boundary value problem is first stated in dimensional form, and an asymptotic analysis is made of the cold horizontal layer. The isoviscous core is analyzed to obtain the stream-function outside the boundary layers in terms of the heat flow. The temperature drop across the hot horizontal layer is determined, and a detailed calculation is given for the case in which the bottom is traction-free. The resulting analytical predictions are compared with experimental and numerical results obtained elsewhere.

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