A note on the multi-α solutions of the upper bounding problem for thermal convection |
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| Authors: | Joe M Straus |
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| Institution: | Space Sciences Laboratory, Laboratory Operations, The Aerospace Corporation, El Segundo, Calif., U.S.A. |
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| Abstract: | The transition to “multi-α” solutions of the upper bounding problem for thermal convection is discussed. For convection in a fluid contained between parallel stress-free perfectly conducting boundaries, the “single-α” solutions of Straus (1973) are used to determine the Rayleigh number R at which the first transition occurs. Two upper bounding problems are treated: one valid for all values of the Prandtl number and one valid only for large Prandtl numbers. A significant difference between the two problems is noted. The former has a transition at R ～ 28200; the latter has no transition within the range of Rayleigh numbers treated here: R ? 2.3 · 105. |
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