Energy-Conserving Truncations for Convection with Shear Flow

Details Energy-Conserving Truncations for Convection with Shear Flow Energy-Conserving Truncations for Convection with Shear Flow

1996-04-03

arxiv.org/abs/chao-dyn/9603019v1

Physics of Fluids 8 (7), 1715-19, July 1996.

Nonlinear Sciences

Chaotic Dynamics

18 pages, 5 Postscript figures, uses RevTeX and epsf. Accepted for publication in Physics of Fluids

Scientific paper

10.1063/1.868956

A method is presented for making finite Fourier mode truncations of the Rayleigh--Benard convection system that preserve invariants of the full partial differential equations in the dissipationless limit. These truncations are shown to have no unbounded solutions and provide a description of the thermal flux that has the correct limiting behavior in a steady-state. A particular low-order truncation (containing 7 modes) is selected and compared with the 6 mode truncation of Howard and Krishnamurti (1986), which does not conserve the total energy in the dissipationless limit. A numerical example is presented to compare the two truncations and study the effect of shear flow on thermal transport.

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