Stability and heat transfer of rotating cryogens. Part 3. Effects of finite cylindrical geometry and rotation on the onset of convection

Abstract

This report presents data describing convection in a rotating cylindrical Bénard cell filled with He I. In particular, convection modes are observed at Rayleigh numbers substantially below those predicted by linear stability analyses for a horizontally infinite layer. Both the Rayleigh numbers associated with the convective onset and the initial-slope measure of heat transport of these modes are found to depend on the rotation rate Ω and the aspect ratio Γ of the cell. A discussion of the relevant literature reveals that these convective modes are probably the same as those observed by Rossby (1969) and are reasonably well characterized by the recent analysis of Buell & Catton (1983) assuming asymmetric modes.

Heat transport measurements in turbulent rotating Rayleigh-Bénard convection

“…The transition to convection from a conduction state occurred at ∆T c ≈ 150 mK and Ra c ≈ 2×10 6 , much lower than the theoretical value of 1.6×10 7 for a laterally-infinite system at this rotation rate [7]. This lower-than-expected transition was observed in early heat-transport experiments [8,9,28] and was later visually identified as a transition to a side-wall traveling-wave state [9,30]. Extrapolating the results in [9] to Ω = 2.88 × 10 4 , one obtains the onset to the traveling state at about 3 × 10 6 , not far from our value of 2 × 10 6 .…”

Local temperature measurements in turbulent rotating Rayleigh-Bénard convection

“…There is a fascinating interplay between heat transport in rotating convection [1][2][3][4][5][6][7][8] and the vortical nature of structures that arise out of thermal boundary layers at the top and bottom of a Rayleigh-Bénard convection cell [9][10][11][12]. Such vortical structures are very familiar in geophysical contexts and have been studied semi-quantitatively in rotating thermal convection experiments with open top surfaces [13].…”

Onset of convection in a moderate aspect-ratio rotating cylinder: Eckhaus–Benjamin–Feir instability

“…The experiments of Rossby (1967) found significant discrepancies with the unbounded theory for the onset of convection, measuring convective heat transfer at Rayleigh numbers much lower than predicted. Buell & Catton (1983) and Pfotenhauer, Niemela & Donnelly (1987), based on linear stability analysis and experiments, proposed that the cause of the discrepancy was due to the presence of lateral confinement. Subsequent experiments, designed to allow for flow visualization (Zhong, Ecke & Steinberg 1991Ning & Ecke 1993), showed that the convective heat transport recorded at Rayleigh numbers below the predicted critical value was due to a so-called convective wall mode, consisting of alternating hot and cold thermal plumes rising and descending in the cylinder sidewall boundary layer, and precessing retrograde with respect to the rotation of the cylinder.…”