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  • FLUID MECHANICS AND HEAT TRANSFER  (2)
  • 1975-1979  (2)
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  • 1
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    Modal equations for cellular convection (1975)
    In:  Other Sources
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    Publication Date: 2019-06-27
    Description: We expand the fluctuating flow variables of Boussinesq convection in the planform functions of linear theory. Our proposal is to consider a drastic truncation of this expansion as a possible useful approximation scheme for studying cellular convection. With just one term included, we obtain a fairly simple set of equations which reproduces some of the qualitative properties of cellular convection and whose steady-state form has already been derived by Roberts (1966). This set of 'modal equations' is analyzed at slightly supercritical and at very high Rayleigh numbers. In the latter regime the Nusselt number varies with Rayleigh number just as in the mean-field approximation with one horizontal scale when the boundaries are rigid. However, the Nusselt number now depends also on the Prandtl number in a way that seems compatible with experiment. The chief difficulty with the approach is the absence of a deductive scheme for deciding which planforms should be retained in the truncated expansion.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Fluid Mechanics; 68; Apr. 29
    Format: text
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  • 2
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    Numerical solutions of single-mode convection equations (1977)
    In:  Other Sources
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    Publication Date: 2019-06-27
    Description: In the Boussinesq approximation, single-mode equations describing thermal convection are constructed by expanding the fluctuating velocity and temperature fields in a complete set of functions (or planforms) of the horizontal coordinates and retaining just one term. Numerical solutions of the single-mode equations are investigated, chief consideration being given to hexagonal planforms. Extensive surveys of steady solutions are presented for various Rayleigh numbers, Prandtl numbers, and horizontal wavenumbers. The dependences on Rayleigh number and Prandtl number at very large Rayleigh number are in satisfactory agreement with the results of asymptotic expansions.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Fluid Mechanics; 79; Jan. 20
    Format: text
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