[M-IS21] Geophysical fluid dynamics-Transfield approach to geoscience

[MIS21-P02] Prandtl number dependence of Rayleigh-Benard convection tightly confined by lateral walls

*Yuji Tasaka^1,3, Takatoshi Yanagisawa^3,1, Ichiro Kumagai², Daisuke Noto⁴ (1.Faculty of Engineering, Hokkaido University, 2.School of Science and Engineering, Meisei University, 3.Japan Agency for Marine-Earth Science and Technology, 4.Department of Earth and Environmental Science, University of Pennsylvania)

Keywords:Thermal convection, Flow transition, Hele-Shaw system

Rayleigh-Benard convection in Hele-Shaw system has great importance to understand heat and mass transfer in fractures for geoscience and environmental studies. The phenomenon has also collected interests from turbulent flow researchers as suppression of thermal turbulence. We investigated intermediate regime between Hele-Shaw regime and 3D thermal turbulence regime termed quasi-Hele-Shaw regime by laboratory experiments and numerical simulations, especially focusing on onset of unsteady behavior of the convection. To elucidate influence of Prandtl number on the phenomena, polymer solutions with different concentrations and liquid gallium were used as test fluids. Systematic parameter studies about Prandtl number (Pr) and Rayleigh-Darcy number (Ra_D) suggested that the transition to unsteady convection obeys different mechanics for the high or low Prandtl number conditions. For the former conditions, because of increase of intrinsic viscosity due to the lateral wall confinement, the transition is similar to that of very high Prandtl number conditions in which unsteadiness is from unevenness of temperature field with small Reynolds numbers. The critical condition for the onset of unsteady convection seems to be given by ε²Ra_D = 1, where ε denotes anisotropy ratio, ε² = D/(12H) with depth and height of the fluid layer, D and H. This dimensionless value is the indication of perturbation from Hele-Shaw approximation. For the low Pr case, the transition behaves quite different manner, and the critical condition is given as ε²Ra_D/Pr = 1. This indicates that the unsteadiness is from inertia of the convective motion unlike the high Pr cases.