Energy-conserving truncations for convection with shear flow

Publisher Website
Google Scholar
Abstract
A method is presented for making finite Fourier mode truncations of the Rayleigh–Bénard 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 [J. Fluid Mech. 170, 385 (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.
All Related Versions