Computer Science
Scientific paper
Dec 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982jfm...125...99t&link_type=abstract
Journal of Fluid Mechanics, vol. 125, Dec. 1982, p. 99-122.
Computer Science
27
Convective Heat Transfer, Flow Velocity, Modal Response, Time Dependence, Boussinesq Approximation, Flow Velocity, Nonlinear Equations, Nusselt Number, Rayleigh Number
Scientific paper
Truncated modal equations are used to study the time evolution of thermal convection. In the Boussinesq approximation these nonlinear equations are obtained by expanding the fluctuating velocity and temperature fields in a finite set of planforms of the horizontal coordinates. Numerical studies dealing with two or three modes with triad interactions are discussed. Rich time dependence was found in these cases: periodic and aperiodic solutions can be obtained, along with various steady solutions. Three-mode solutions reproduce the qualitative appearance of spoke-pattern convection as observed in experiments at high Prandtl numbers. Though the values of the periods of the time-dependent solutions do not agree with those of the experiments, their variation with Rayleigh number compares favorably. Except at the highest Rayleigh number considered (10,000,000), the theoretical Nusselt numbers agree well with experiment.
Gough Douglas O.
Spiegel Edward A.
Toomre Juri
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