Heat transport measurements in turbulent rotating Rayleigh-Bénard convection

Abstract

We present experimental heat transport measurements of turbulent Rayleigh-Bénard convection with rotation about a vertical axis. The fluid, water with a Prandtl number (sigma) of about 6, was confined in a cell with a square cross section of 7.3 x 7.3 cm2 and a height of 9.4 cm. Heat transport was measured for Rayleigh numbers 2 x 10(5)<Ra<5 x 10(8) and Taylor numbers 0<Ta<5 x 10(9). We show the variation in normalized heat transport, the Nusselt number, at fixed dimensional rotation rate OmegaD, at fixed Ra varying Ta, at fixed Ta varying Ra, and at fixed Rossby number Ro. The scaling of heat transport in the range of 10(7) to about 10(9) is roughly 0.29 with a Ro-dependent coefficient or equivalently is also well fit by a combination of power laws of the form a Ra1/5+b Ra1/3. The range of Ra is not sufficient to differentiate single power law or combined power-law scaling. The data are roughly consistent with an assumption that the enhancement of heat transport owing to rotation is proportional to the number of vortical structures penetrating the boundary layer. We also compare indirect measures of thermal and Ekman boundary layer thicknesses to assess their potential role in controlling heat transport in different regimes of Ra and Ta.

Turbulent convection in liquid metal with and without rotation

“…The agreement between heat transfer measurements in nonrotating liquid metal and the inertial scaling [4], shown in Fig. 2B, suggests that the transition between rotationally constrained and weakly rotating convection should occur when Ro c ≈ 1 ( [7]).…”

“…The dashed line in Fig. 2B shows the inertial scaling law [4] for the median experimental value of Pr = 0:025. Experimental heat transfer data trend with this scaling law, but are 7% less than predicted on average.…”

“…23,25,36). Essentially, the difference between scaling laws [1] and [4] is that in the former the thermal boundary layer thickness is determined by its own marginal stability, whereas in the latter the thermal boundary layer thickness is set by the strength of interior turbulence. Rotation suppresses convection, such that the onset of convection is delayed, Ra c ∝ E −4=3 , where Ra c is the critical Rayleigh number, and, in many cases, less heat is transported by rotating convection than by nonrotating convection.…”

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].…”

“…This process depends strongly on Ra and Pr [11] and the boundary conditions [19]. Liu and Ecke [7] showed that this increase in Nu can be presented in several ways, as the rotation rate can be expressed by the Taylor Ta number, which measures the effect of the rotational Coriolis force, and the Rossby Ro number, which indicates the relation between the buoyancy and Coriolis forces. Here we choose the latter since Ro indicates when Ekman pumping effects become important with respect to buoyancy effects [12].…”