Ikuro Sumita $^{a}$, Peter Olson $^{b}$
$^{a}$ Department of Earth Sciences, Kanazawa University, Kanazawa, Japan $^{b}$ Department of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, Maryland, USA
sumita@hakusan.s.kanazawa-u.ac.jp
Introduction: Flow in the Earth's fluid core is dominated by rotation and the Ekman number is very small, of the order of $10^{-15}$. Rotation inhibits convection, and consequently, thermal convection in the Earth's core occurs at high Rayleigh number. Convection under low Ekman number is characterized by fine scales, and that at high Rayleigh number by turbulence. The study of convection under such conditions forms the basis of understanding core flow. However because of the dominance of non-linearity, our understanding of these flows are still insufficient. In the recent years, there have been several experimental studies focusing on convection at low Ekman numbers ($Ek = 10^{-7}$ to $10^{-6}$) and at high Rayleigh numbers (up to 50 times critical), using water (Sumita and Olson, 2000), and gallium (Aubert et al., 2001), as the working fluid. The parameter range of these experiments are about an order of magnitude closer to that of the Earth, compared to that which can be achieved by present numerical computations. Furthermore, because there are no effects arising from numerical diffusion and finite grids, it is better suited to study fine-scaled turbulence. Sumita and Olson (2000) studied convection at Ekman number of $4.7 \times 10^{-6}$ and $Ra/Rac < 50$, and found that the flow was dominated by geostrophic turbulence. Here, we extend their study to even higher Rayleigh numbers to study the asymptotic regime of geostrophic turbulence. To do so, we use 1cSt silicone fluid, which enables us to study convection up to $Ra = 1.2 \times 10^{10} (500 Ra_c)$ at the same Ekman number $4.7 \times 10^{-6}$. The Prandtl number of 1cSt silicone fluid is 13.9, and weakly non-linear theory (Zhang, 1992) show that the flow would not differ much from that of water ($Pr = 7.1$). Experimental Method: We use a copper hemispherical shell of an outer diameter of 30 cm and an inner diameter of 10 cm, and spin it at a rotation rate of 206 rpm. We maintain the temperature of the inner boundary (ICB) at a lower temperature than the outer boundary (CMB) to obtain the thermal buoyancy needed to drive convection. Temperature in the fluid is measured using thermistor probes. Flow velocity is measured by using neutrally buoyant tracers of fluorescent methanol solution. Results: Average temperature structure: Radial temperature profile indicate that there is a significant thermal boundary layer near the ICB, whose thickness decreases with Rayleigh number. Radial temperature gradient elsewhere is small and becomes nearly isothermal at the highest Rayleigh numbers. Temporal variation of temperature: Temperature fluctuates irregularly, and its amplitude decreases towards CMB, indicating that it is determined by the temperature gradient there. The amplitude scales as 0.6 power of the heat flow, which agrees with that predicted by the scaling of Cardin and Olson (1994). High frequency component increases with Rayleigh number, suggesting larger advection of radial plumes by the zonal flow. Statistical properties of temperature-times series data can be interpreted as a consequence of enlarged cyclonic voritices (as compared to anticyclonic vortices) that are advected westward by the mean zonal flow. Flow velocity: Zonal flow is westward, and is about 3mm/s at $Ra/Rac = 277$, which is about an order of magnitude larger than that at $Ra/Rac = 44$ (Sumita and Olson, 2000). Layered convection: We also studied layered convection with the silicone oil in the inner layer and the water in the outer layer and measured how the total heat flow changes with the thickness ratio, under the fixed radial temperature difference. We find that heat flow is at a minimum when there is a thin layer above the ICB, but increases monotonically with the thickness of the inner layer by about a factor of 2. A model of heat transfer in a layered system shows that this result arises from sphericity. Conclusions: Convection up to $Ra/Rac=500$ can be understood by the scaling of geostrophic turbulence. Heat flow measurement of a layered convection in a spherical shell show that the heat transfer is strongly inhibited when there is a thin dense layer above the ICB, and can be relevant to the Earth's core. References: Aubert, J. D. et al., 2001. {\it Phys. Earth Planet. Inter.}, {\bf 128}, 51-74. Cardin, P. and P. Olson, 1994. {\it ibid.}, {\bf 82}, 235-259. Sumita, I. and P. Olson, 2000. {\it ibid.}, {\bf 117}, 153-170. Zhang, K. 1992. {\it J. Fluid Mech.}, {\bf 236}, 535-556.