[O-08] Kitchen Earth Science: its potential for producing diverse goals by hands-on experiments

[O08-P10] Analysis of thermal convection pattern in two immiscible liquid layers with an undeformed horizontal interface

★Invited Papers

*Mizuki Nakamura¹, Hiroaki Ito², Hiroyuki Kitahata² (1.Graduate School of Science and Engineering, Chiba University, 2.Graduate School of Science, Chiba University)

Keywords:reaction-diffusion system, pattern formation, fluid mechanics, numerical calculation, two-layer convection, mantle

Rayleigh-Bénard convection is one of the most famous non-equilibrium phenomena that occur in systems with a temperature difference between the upper and lower boundaries. This type of convection was first observed in the 1900s, when H. Bénard made experiments on the convection by heating a horizontal layer of liquid from below. Rayleigh later established a theoretical framework of the convection mechanism in a single-layer system. From their names, this convection phenomenon is called Rayleigh-Benard convection. Rayleigh-Bénard convection is driven by buoyancy caused by temperature differences, and it is observed in various natural phenomena, including the Sun, the Earth's interior, and the atmosphere and oceans. The onset of convection is determined by the Rayleigh number, a dimensionless parameter related to the buoyancy and thermal diffusion. If the Rayleigh number of the system is less than a critical value, convection does not occur. In contrast, when the Rayleigh number is above it, convection emerges.

The study of the two-layer Rayleigh-Bénard convection started with geological interest and drew interest due to the various bifurcation phenomena. In two-layer systems with an undeformed horizontal interface, Rayleigh-Bénard convection can be coupled either mechanically or thermally. The vertical flow directions in the two layers are opposite in the mechanical coupling, whereas they are the same in the thermal coupling. The stability of the coupling pattern depends on the factors such as the ratios of depth, viscosity, and density between the layers, and the temperature differences. The smallest critical Rayleigh number for a symmetric two-layer thermal convection system with an undeformed horizontal interface is 17610[1], at which mechanical coupling appears. The critical Rayleigh number at which thermal coupling appears is reported to be even larger, at 20731[2]. Linear stability analysis calculations yield them.

We study the selection mechanism of thermal convection patterns in a symmetric two-layer system with an undeformed horizontal interface by varying the initial conditions in a two-dimensional hydrodynamic simulation. In this system, both the coupling patterns can be stable. Simulations were conducted with initial conditions corresponding to each coupling type. Based on the simulation results, we investigated the selection mechanism of the coupling patterns. Furthermore, we discuss the specific factors determining the coupling pattern in the viewpoint of the heat transportation.

Reference:
[1] S. Chandrasekhar, Hydrodynamic and Hydromagnetic stability, Dover Books on Physics (Dover Publications, 1981).
[2] S.Rasenat, F. Busse, and I. Rehberg, J. Fluid Mech. 199, 519 (1989).