A. Namiki
Department of Earth Sciences, Kanazawa University, Kanazawa, JAPAN.
namiki@earth.s.kanazawa-u.ac.jp
Recent seismological observations and geo-dynamical investigations have revealed that D$''$ is chemically separated and might convect separately from the overlying mantle. A chemically separated convecting layer at the bottom of the mantle will essentially affect the thermal state of the mantle convection, which suppresses the heat transfer from the core to the mantle and modify the radial temperature profile of the Earth. In this poster, we simultaneously measure the interfacial temperature and heat flux of the two-layered convection using immiscible fluids (H$_2$O solution and castor or silicone oil), and compare them using a simple scaling law. The experiment is conducted in a cylindrical cell. A silicone rubber film heater is installed on the backside of the bottom plate. DC power is supplied to maintain a constant temperature at the bottom plate. We measured the DC power and calculated the heat flux. Three small movable thermistor probes are placed inside the cell in order to measure the vertical temperature profile of the convecting fluid. We defined the interfacial temperature from the intersection of two temperature profiles measured from upper and lower boundaries. Assuming the well known relation, $Nu \sim \gamma Ra^{\beta}$, where $ 0.28< \beta < 0.30$ and $0.12 < \gamma < 0.21$, the ratio of the temperature difference between two layers (layer 1 and 2) can be expressed as, \begin{equation} \frac{\Delta T_2}{\Delta T_1} \sim \left (\frac{\alpha_1 C_{p1} \eta_2}{\alpha_2 C_{p2} \eta_1} \right )^{\frac{\beta}{1+\beta}} \left (\frac{k_1 \rho_1}{k_2 \rho_2} \right )^{\frac{1-\beta}{1+\beta}} \left (\frac{L_2}{L_1} \right)^{\frac{1-3\beta}{1+\beta}}. \end{equation} Our measurements show a good agreement to the calculated interfacial temperature with $\beta \sim 0.29$, although some experiments are conducted under the condition of $B = \Delta \rho / \rho \alpha \Delta T < 1$, where the interface have undulations. The experiments under $B>1$ indicate that the measured Nusselt numbers show a good agreement with the well known $Nu-Ra$ relation based on one layer convection. Nusselt numbers under $B<1$, however, show a different curve, $Nu \sim 0.25 Ra^{0.3}$; i.e., the measured $Nu-Ra$ relation also can be described by a power law with the same exponent $\beta$ but with a larger amplitude $\gamma$. In general, the layering of convection suppresses the heat transfer comparing the whole layer convection. When the material properties of the mantle and D$''$ are the same, separately convecting mantle and D$''$ can transfer only 40 \% of heat transferred by the whole layer mantle convection. If the viscosity of D$''$ is extremely smaller than that of the mantle, however, the reduction of heat transfer is suppressed in a small range. Here, the thickness of D$''$ varies horizontally, which suggests that the topographical coupling arises between the mantle and D$''$. The heat transfer would be enhanced by the topographical coupling. The total heat transfer may exceed that transfered by one layered mantle convection. It has been recognized that the estimated current global heat loss exceeds the sum of the heat production by radioactive elements and secular cooling of the Earth. The source of this discrepancy might be less viscous D$''$ with small density difference from the mantle transferring excess heat from the core.