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Time‐dependent convection in elongated Rayleigh‐Benard cells
Author(s) -
Christensen Ulrich R.
Publication year - 1987
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/gl014i003p00220
Subject(s) - convection , prandtl number , rayleigh number , rayleigh–bénard convection , convection cell , physics , mechanics , rayleigh scattering , wavelength , natural convection , geophysics , combined forced and natural convection , optics
The onset of time‐dependence and some subsequent transitions in two‐dimensional Rayleigh‐Bénard cells of aspect ratios a=2.5 and a=4 are studied numerically for a Boussinesq fluid of infinite Prandtl number. Oscillatory convection starts at a Rayleigh number of only 21,000 (a=2.5) or 12,000 (a=4.0) for stress‐free boundaries. Above Ra=100,000 the cells with a=4.0 break down into several short cells, whereas single cells with a=2.5 remain stable to at least Ra=500,000. With rigid boundaries the tendency towards break‐up into short cells is found to be more pronounced. Long‐wavelength cells, modulated by travelling boundary‐layer instabilities, appear to be a likely form of convection in the earth's mantle.