Computer Science
Scientific paper
Apr 1975
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975jfm....68..695g&link_type=abstract
Journal of Fluid Mechanics, vol. 68, Apr. 29, 1975, p. 695-719.
Computer Science
42
Asymptotic Methods, Benard Cells, Boussinesq Approximation, Convection Currents, Incompressible Fluids, Boundary Layer Equations, Free Boundaries, Nusselt Number, Prandtl Number, Rayleigh Number
Scientific paper
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.
Gough Douglas O.
Spiegel Edward A.
Toomre Juri
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