Thermal Convection between Sloping Parallel Boundaries

The effect of sloping boundaries on thermal convection is studied theoretically and experimentally in the context of a model in which fluid is contained in a differentially heated rectangular box of small aspect ratio (depth/length), inclined at an angle 8 to the vertical. Like its two limiting cases, Benard convection and convection in the vertical slot, there is a steady laminar twodimensional mean flow at low Rayleigh numbers which becomes unstable as this parameter is increased. The types of instability observed depend crucially on 8 . In our experiments with water there are some secondary motions which apparently arise from a new mechanism which is present in neither of the limiting cases. The measurements of transition points, critical wavelengths, and frequencies indicate that for 90 -> S 10 (bottom plate hotter) longitudinal convective modes of instability with axes oriented parallel to the mean upslope-downslope circulation, are dominant. Near the vertical, IO'> S>-IO, travelling transverse modes are the most unstable. Longitudinal modes are again found for 10 -, -> q oa (bottom plate hotter). The theoretical analysis of the stability problem suggests that these last instabilities are generated by a buoyancy excess. This is maintained by advection of the mean upstream temperature gradient by the upstream velocity. This upstream velocity can be generated either by upstream