Wave number selection and large-scale-flow effects due to a radial ramp of the spacing in Rayleigh-Benard convection

We present experimental results for wave numbers q(s) selected in a thin horizontal fluid layer heated from below. The cylindrical sample had an interior section of uniform spacing d = d(o) for radii r < r(o) (Gamma(o) = r(o)/d(o) = 43) and a ramp d(r) for r > r(o). For Rayleigh numbers R-o > R-c = 1708 in the interior, straight or slightly curved rolls with an average [q(s)] = (q) over tilde(c) + alpha epsilon(o)(epsilon(o) = R-o/R-c - 1) and (q) over tilde(c) < q(c) = 3.117 were selected, and q(s) varied on two length scales approximately equal to Gamma(o) and to four roll wavelengths. For epsilon less than or similar to 0.03 and epsilon less than or similar to 0.18 the pattern repeatedly formed defects.