Rayleigh-Benard convection in the presence of a radial ramp of the Rayleigh number

We present experimental results for pattern formation in a thin horizontal fluid layer heated from below. The fluid was SF6 at a pressure of 20.0 bar with a Prandtl number of 0.87. The cylindrical sample had an interior section of uniform spacing d = d(0) for radii r < r(0) and a ramp d( r) for r > r0. For Rayleigh numbers R-0 > R-c in the interior, straight or slightly curved rolls with an average wavenumber < k(s)> = (k) over tilde (c) + k(1)epsilon(0) (epsilon(0) = R-0/R-c - 1) with k(1) similar or equal to 0.8 were selected. The critical wavenumber (k) over tilde (c) depended sensitively on the cell spacing. For the largest (k) over tilde (c) the patterns were skewed-varicose unstable and dislocation pairs were generated repeatedly in the interior and for all e. For slightly smaller (k) over tilde (c) time-independent rolls were stable for epsilon less than or similar to 0.15, but for larger epsilon the skewed-varicose instability was encountered near the sample centre and dislocation pairs were formed repeatedly for all samples. When stationary rolls were stable, their slight curvature and the width of their wavenumber distribution slowly increased with e. This led to a complicated shape and overall broadening of the structure factor S( k). For epsilon less than or similar to 0.05 the inverse width xi(2) of S(k) was roughly constant and presumably limited by the finite sample size, but for larger epsilon we found xi(2) proportional to epsilon(-0.5).