Turbulent rotating convection confined in a slender cylinder: The sidewall circulation

Abstract

Recent studies of rotating Rayleigh-Bénard convection at high rotation rates and strong thermal forcing have shown a significant discrepancy in total heat transport between experiments on a confined cylindrical domain on the one hand and simulations on a laterally unconfined periodic domain on the other. This paper addresses this discrepancy using direct numerical simulations on a cylindrical domain. An analysis of the flow field reveals a region of enhanced convection near the wall, the sidewall circulation. The sidewall circulation rotates slowly within the cylinder in anticyclonic direction. It has a convoluted structure, illustrated by mean flow fields in horizontal cross-sections of the flow where instantaneous snapshots are compensated for the orientation of the sidewall circulation before averaging. Through separate analysis of the sidewall region and the inner bulk flow, we find that for higher values of the thermal forcing the heat transport in the inner part of the cylindrical domain, outside the sidewall circulation region, coincides with the heat transport on the unconfined periodic domain. Thus the sidewall circulation accounts for the differences in heat transfer between the two considered domains, while in the bulk the turbulent heat flux is the same as that of a laterally unbounded periodic domain. Therefore, experiments, with their inherent confinement, can still provide turbulence akin to the unbounded domains of simulations, and at more extreme values of the governing parameters for thermal forcing and rotation. We also provide experimental evidence for the existence of the sidewall circulation that is in close agreement with the simulation results.

Subcritical turbulent condensate in rapidly rotating Rayleigh–Bénard convection

“…Note that de Wit et al (2020) also measured the drift frequency as a function of Ra and found the following fit: ω d ≈ −6 × 10 −10 Ra 1.16±0.06 E (using our rotation units). Using the same approach as in section 3, we measured the drift frequency in our simulations below the onset of the bulk mode and in figure 4(c) we compare the results with the fit of de Wit et al (2020). The results clearly bridge the gap between the onset theoretical value derived by Herrmann & Busse (1993) and the highly turbulent scaling found by de Wit et al (2020).…”

“…Despite this, we show here that these modes bear all the hallmarks of topologically protected states. We first show -in a cylindrical geometry -that these modes are robust with respect to secondary instabilities and to a turbulent bulk state as in the experiments (de Wit et al 2020;Zhang et al 2020) by gradually increasing the Rayleigh number until the bulk becomes turbulent. Second, we show that these states persist in the presence of different types of barriers, and show that the wall modes happily follow whatever boundary geometry is provided.…”

“…Our work is motivated in part by the zonal currents found independently by two groups in high Rayleigh number experiments and simulations on rapidly rotating convection in a right circular cylinder rotating with constant angular velocity about its vertical axis (de Wit et al 2020;Zhang et al 2020). While the results differ in detail both groups observe an intense zonal flow that precesses with respect to the rotating frame and is nearly indifferent to the bulk turbulent state.…”

“…where u ≡ (u, v, w) is the velocity, p is the pressure and θ is the temperature fluctuation relative to the conduction profile that varies linearly with respect to the vertical Figure 1. Summary of the runs performed for this study (full symbols ), along with past studies (Ecke et al 1992;Scheel et al 2003;de Wit et al 2020;Zhang et al 2020). The blue line corresponds to the onset of the wall mode while the red line corresponds to the onset of the bulk mode.…”

“…Recent experiments and simulations have shown the emergence of a boundary zonal flow in confined rotating Rayleigh-Bénard convection (Kunnen et al 2011;de Wit et al 2020;Zhang et al 2020). However, a link between this flow and the wall modes was not explicitly made.…”