Rayleigh–Bénard convection in the presence of a radial ramp of the Rayleigh number

Abstract

We present experimental results for pattern formation in a thin horizontal fluid layer heated from below. The fluid was SF 6 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 > r 0 . For Rayleigh numbers R 0 > R c in the interior, straight or slightly curved rolls with an average wavenumber k s = kc + k 1 ε 0 (ε 0 ≡ R 0 /R c − 1) with k 1 0.8 were selected. The critical wavenumber kc depended sensitively on the cell spacing. For the largest kc the patterns were skewed-varicose unstable and dislocation pairs were generated repeatedly in the interior and for all ε. For slightly smaller kc time-independent rolls were stable for ε 0.15, but for larger ε the skewedvaricose 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 ε. This led to a complicated shape and overall broadening of the structure factor S(k). For ε 0.05 the inverse width ξ 2 of S(k) was roughly constant and presumably limited by the finite sample size, but for larger ε we found ξ 2 ∝ ε −0.5 .

Domain chaos puzzle and the calculation of the structure factor and its half-width

“…Laveder et al demonstrated that additive white noise intended to mimic the effect of wall defects decreases ν to the value of ν ef f measured experimentally provided that the noise level is sufficiently large [20]. Recent unpublished experiments in our group using a sample with a radially ramped spacing [21,22] render the side-wallinjected defect idea an unlikely explanation. On the basis of numerical simulation using a SH equation Cross et al proposed that the finite size of the experimental convection sample decreases the effective value of ν [23].…”