Breakdown of large-scale circulation in turbulent rotating convection

Abstract

Turbulent rotating convection in a cylinder is investigated both numerically and experimentally at Rayleigh number Ra = 10 9 and Prandtl number σ = 6.4. In this Letter we discuss two topics: the breakdown under rotation of the domain-filling large-scale circulation (LSC) typical for confined convection, and the convective heat transfer through the fluid layer, expressed by the Nusselt number. The presence of the LSC is addressed for several rotation rates. For Rossby numbers Ro 1.2 no LSC is found (the Rossby number indicates relative importance of buoyancy over rotation, hence small Ro indicates strong rotation). For larger Rossby numbers a precession of the LSC in anticyclonic direction (counter to the background rotation) is observed. It is shown that the heat transfer has a maximal value close to Ro = 0.18 being about 15% larger than in the non-rotating case Ro = ∞. Since the LSC is no longer present at this Rossby value we conclude that the peak heat transfer is independent of the LSC.

Prandtl-, Rayleigh-, and Rossby-Number Dependence of Heat Transport in Turbulent Rotating Rayleigh-Bénard Convection

“…Also shown are the DNS results from Ref. [15]; these data agree rather well with the experimental data at nearly the same Pr and Ra. One sees that the enhancement of Nu at large Ro is nearly independent of Pr, but as Ro decreases below unity a strong Pr dependence manifests itself.…”

“…However, at modest rotation rates, experiments [9][10][11] and numerical simulations [12][13][14][15] have shown that under certain conditions the heat transport can also be enhanced, before it rapidly decreases for stronger rotation. This enhancement has been ascribed to Ekman pumping [13,[16][17][18]: Because of the rotation, rising or falling plumes of hot or cold fluid are stretched into vertical vortices that suck fluid out of the thermal boundary layers (BL) adjacent to the bottom and top plates.…”

“…The equations have been made nondimensional by using, next to L and Á, the freefall velocity U ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffi ffi gÁL p . The simulations were performed on a grid of 129 Â 257 Â 257 nodes, respectively, in the radial, azimuthal and vertical directions, allowing for a sufficient resolution of the small scales both inside the bulk of turbulence and in the BLs (where the grid-point density has been enhanced) for the parameters employed here [14,15]. Nu is calculated as in Refs.…”

Laboratory-numerical models of rapidly rotating convection in planetary cores

“…There is a slight overshoot of rotating heat transfer beyond the RBC scalings for Ra Ra T (cf. Niiler & Bisshopp 1965; Julien et al 1996;Kunnen et al 2008). However, this effect is strong only at relatively high E. In fact, our data shows that the overshoot becomes small for E 10 −5 .…”

Optimal Prandtl number for heat transfer in rotating Rayleigh–Bénard convection

“…Previous experimental [7]- [13] and numerical studies [11]- [16] at constant Ra and Pr have shown that at moderate rotation rates the convective heat transfer is higher than for the nonrotating case. This heat transport enhancement with respect to the non-rotating case has been ascribed to Ekman pumping [8], [10]- [13], [15]- [18].…”