Journal of Fluid Mechanics

Convective versus absolute instability in mixed Rayleigh–Bénard–Poiseuille convection

a1 Laboratoire de Mécanique des Fluides et d'Acoustique, UMR CNRS 5509, Ecole Centrale de Lyon-Université Claude Bernard Lyon I, BP163, 69131 Ecully cedex, France
a2 IMHEF-Laboratoire de Mécanique des Fluides, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland


Transition from convective to absolute instability in Rayleigh–Bénard convection in the presence of a uni-directional Poiseuille flow is studied. The evaluation of the long-time behaviour of the Green function in the horizontal plane allows the determination of regions of convective and absolute instability in the Rayleigh–Reynolds number plane as a function of Prandtl number. It is found that the mode reaching zero group velocity at the convective–absolute transition always corresponds to transverse rolls, while the system remains convectively unstable with respect to pure streamwise (longitudinal) rolls for all non-zero Reynolds numbers. Finally, the roll pattern within the entire wave packet and in particular near its centre is elucidated and possible connections between experiments and our findings are discussed.

(Received April 4 1998)
(Revised September 7 1998)