We examine the onset of Rayleigh-Bénard convection in a horizontal fluid layer with an imposed weak shear flow. Convection patterns in the form of traveling transverse rolls and stationary longitudinal rolls are considered. The investigation is performed in the framework of amplitude equations which allow for slow variations of the order parameter field both in the streamwise coordinate and in time. By invoking the concept of absolute and convective instability of the basic state, it is shown that a nontrivial selection of the most unstable mode takes place. The role of noise upon the selection process is investigated by considering the spatial growth exponents for both types of structures.

• Received 18 February 1994

DOI:https://doi.org/10.1103/PhysRevE.50.1219