A Note on the Criteria for the Onset of Stationary Parallel-Plate Convection Subject to Mean Vertical Motion

Abstract

The Benard problem is extended to include the effects of perfectly conducting, but porous, boundaries permitting an average vertical mass flux, characterized by a Peclet number, through the system. The linear stability problem for the onset of stationary convection is solved using a power series technique and it is found that the stability of the system increases for large absolute values of the Peclet number. A detailed comparison with the work of Krishnamurti reveals contradictory results for the magnitude of the horizontal wavenumber as a function of the Péclet number, as well as for the dependence of the stability upon the Prandtl number. These discrepancies and their possible causes are discussed in some detail.