[M-IS16] 地球流体力学：地球惑星現象への分野横断的アプローチ

[MIS16-P01] 狭く閉じられた空間での熱対流のプラントル数への依存性

*柳澤 孝寿^1,5、亀山 真典^2,1、能登 大輔³、熊谷 一郎⁴、田坂 裕司^5,1 (1.国立研究開発法人海洋研究開発機構、2.愛媛大学地球深部ダイナミクス研究センター、3.ペンシルバニア大学、4.明星大学理工学部、5.北海道大学大学院工学研究院)

キーワード：熱対流、プラントル数、形状、パターン

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.