Experimental and numerical studies of convection in a rapidly rotating spherical shell

Abstract

Thermal convection in a rapidly rotating spherical shell is investigated experimentally and numerically. The experiments are performed in water (Prandtl number P=7) and in gallium (P=0.025), at Rayleigh numbers R up to 80 times the critical value in water (up to 6 times critical in gallium) and at Ekman numbers E∼10−6. The measurements of fluid velocities by ultrasonic Doppler velocimetry are quantitatively compared with quasi-geostrophic numerical simulations incorporating a varying β-effect and boundary friction (Ekman pumping). In water, unsteady multiple zonal jets, weaker in amplitude than the non-axisymmetric flow, are experimentally observed and numerically reproduced at moderate forcings (R/Rc<40). In this regime, zonal flows and vortices share the same length scale. Gallium experiments and strongly supercritical convection experiments in water correspond to another regime. In these turbulent flows, the zonal motion amplitude U dominates the non-axisymmetric motion amplitude Ũ. As a result of the reverse cascade of kinetic energy, the characteristic Rhines length scale $\ell_{\beta} \,{\sim}\, \sqrt{\overline{U}/\beta}$ of zonal jets emerges, and the boundary friction becomes the main brake on the growth of the zonal flow. A scaling law U ∼ Ũ4/3 is then derived and verified both numerically and experimentally.

Reynolds stresses and mean fields generated by pure waves: applications to shear flows and convection in a rotating shell

“…Our approach relies on the use of a simplified two-dimensional QG convection model which has to be solved in the equatorial annulus (figure 5a). This model is similar to those developed by Aubert, Gillet & Cardin (2003), Morin & Dormy (2004, Cole (2004), Gillet & Jones (2006) and Gillet et al (2007). Whereas systematic comparisons with corresponding experiments have been given in this latter paper, systematic comparisons of these QG models with realistic threedimensional numerical models, such as Simitev & Busse (2003), have been confined to the linear regime (Aubert et al 2003;Cole 2004;Gillet et al 2007).…”

“…This model is similar to those developed by Aubert, Gillet & Cardin (2003), Morin & Dormy (2004, Cole (2004), Gillet & Jones (2006) and Gillet et al (2007). Whereas systematic comparisons with corresponding experiments have been given in this latter paper, systematic comparisons of these QG models with realistic threedimensional numerical models, such as Simitev & Busse (2003), have been confined to the linear regime (Aubert et al 2003;Cole 2004;Gillet et al 2007). In order to fill this gap, we will present new 'benchmarking' results from the three-dimensional code of Tilgner & Busse (1997) and Simitev & Busse (2003).…”

Oscillatory instability and fluid patterns in low-Prandtl-number Rayleigh-Bénard convection with uniform rotation

“…The estimated value of P r for Earth's molten core 36 is approximately equal to 0.1. The molten outer core and the inner solid core are separated by a transition zone, which itself is in liquid state.…”

“…Low-Prandtl-number convection [33][34][35][36][37][38] is relevant for geophysical 39 and astrophysical 40 problems. The estimated value of P r for Earth's molten core 36 is approximately equal to 0.1.…”

Turbulent convection in liquid metal with and without rotation

“…Nakagawa (26) and Aurnou and Olson (27) also investigate rotating RBC in mercury and gallium, but their studies are limited to convection near onset. Several experiments have been performed using liquid metals in spinning spherical containers, in which convection occurs in response to centrifugal acceleration (28)(29)(30). These studies, although important for understanding global convection dynamics in planetary cores, may not be well controlled thermally (31).…”