It is well known that if the variation with temperature of viscosity is taken into account, the onset of convection in an infinite layer of fluid that is heated from below takes the form of hexagonal convection cells. It is also well known that in a sufficiently strong shear flow, rolls aligned with the flow direction are the preferred mode of convection. Here the process by which a steady or unsteady shear flow de- stroys the usual hexagonal cell pattern is investigated. The critical size of the shear flow that enables rolls to be established at the onset of convection is determined for the case when the stress is prescribed at the boundaries.

• Received 13 March 1995

DOI:https://doi.org/10.1103/PhysRevE.52.3687