PATTERN SELECTION AT THE ONSET OF RAYLEIGH-BENARD CONVECTION IN A HORIZONTAL SHEAR-FLOW

We examine the onset of Rayleigh-Benard convection in a horizontal flu id layer with an imposed weak shear flow. Convection patterns in the f orm of traveling transverse rolls and stationary longitudinal rolls ar e considered. The investigation is performed in the framework of ampli tude equations which allow for slow variations of the order parameter field both in the streamwise coordinate and in time. By invoking the c oncept of absolute and convective instability of the basic state, it i s shown that a nontrivial selection of the most unstable mode takes pl ace. The role of noise upon the selection process is investigated by c onsidering the spatial growth exponents for both types of structures.