[M-IS16] Geophysical fluid dynamics-Transfield approach to geoscience

[MIS16-P01] Prandtl number dependence of confined thermal convection

*Takatoshi Yanagisawa^1,5, Masanori Kameyama^2,1, Daisuke Noto³, Ichiro Kumagai⁴, Yuji Tasaka^5,1 (1.Japan Agency for Marine-Earth Science and Technology, 2.Geodynamics Research Center, Ehime University, 3.University of Pennsylvania, 4.School of Science and Engineering, Meisei University, 5.Faculty of Engineering, Hokkaido University)

Keywords:thermal convection, Prandtl number, geometry, pattern

We explored thermal convection of various Prandtl numbers in confined rectangular geometries whose one horizontal scale is extremely shorter than the hight. These situations are ubiquitous in the field of Earth science, from the surface to the inner core. Some of the examples are, water flow in ice sheet or geothermal network, magma flow in dikes or sills, and liquid metal flow in the solid inner core. The Prandtl number (Pr), which is the ratio of momentum diffusion (viscosity) to thermal diffusion, varies from over 100 (magma) to 1 (water) and to under 0.1 (liquid metal). We conducted three-dimensional direct numerical simulations by systematically varying the Pr, and compared some of the results with our laboratory experiments by using xanthan-gum water solution, water, and liquid gallium. The critical Rayleigh number (Ra) for the onset of convective motion increases due to the narrowness of the gap. We confirmed that the convection behavior has little dependence on Pr from the onset of convection to the formation of steady cells. On the other hand, distinct dependency of behavior on Pr is observed when the flow shows time dependency. For higher Pr (> 10), the flow pattern consists of oscillating corner rolls near the sidewalls and steady slender cells at the central region. For lower Pr (< 1), the pattern consists of horizontally elongated swinging cells. It is summarized that two types of time dependency are identified; one is local (high Pr) and the other is global (low Pr) motion. Gradual change of pattern is observed in the intermediate range of Pr.