Transverse-roll global modes in a Rayleigh-Benard-Poiseuille system with streamwise variable heating

The effect of a spatially inhomogeneous heating of the bottom wall in Rayle igh-Benard-Poiseuille convection is studied for slow streamwise variations of the temperature profile. The problem is defined by the constant Reynolds number of the Poiseuille through flow, assumed to be low (typically less t han or equal to 10), the constant Prandtl number, and the spatial evolution of the Rayleigh number R(X), assumed to be subcritical everywhere except i n a limited region around its single maximum R-t. In this initial study, al l spanwise inhomogeneities such as side walls or spanwise variable heating are neglected to obtain two-dimensional (transverse roll) global mode solut ions by means of WKBJ asymptotics. The resulting frequency selection yields , at leading order, a global mode frequency equal to the local absolute fre quency omega (t) at the streamwise location where the Rayleigh number is ma ximum, with higher-order corrections for non-parallelism. These allow the d etermination of critical values of R-t for global instability as a function of the profile of the local Rayleigh number R(X) and of Prandtl and Reynol ds numbers. (C) 2001 Editions scientifiques et medicales Elsevier SAS.