[S-CG48] Planetary interiors revealed by exploration, experiments, and simulations

[SCG48-P04] The analysis of the scaling exponent of the Nusselt number in Rayleigh–Benard convection with infinite Prandtl number

*Daishi Iwaguro¹, Masaki Yoshida¹ (1.Ritsumeikan Univercity)

Keywords:Infinite Prandtl number, Benard convection, Nusselt number, Scaling exponent

Rayleigh-Benard convection is a phenomenon in which thermal convection occurs when the lower part of a horizontal fluid layer is heated while the upper part is cooled, provided that a critical condition is met. In this study, we investigate this phenomenon by focusing on thermal convection with an infinite Prandtl number and examine in detail the scaling exponent of the Nusselt number (Nu). In general, for thermal convection with an infinite Prandtl number, such as mantle convection in the Earth's interior, the scaling exponent Nu ∝ Ra^1/3 is widely applied to describe the dependence of the Nusselt number on the Rayleigh number (Ra). However, in turbulent thermal convection with a finite Prandtl number, the scaling exponent varies depending on the Prandtl number (Pr) and Rayleigh number, and many aspects remain unresolved, particularly regarding the applicability of different scaling exponents and the behavior at their boundary regions. Furthermore, for laminar thermal convection, although analytical approaches based on conventional steady boundary layer theory exist, issues related to velocity distribution and theoretical inconsistencies have been pointed out, highlighting the need for further refinement. In this study, we conduct numerical simulations of thermal convection with an infinite Prandtl number over a broad range of Rayleigh numbers, from near the critical Rayleigh number to Ra = O(10⁶), to investigate the dependence of the Nusselt number on the Rayleigh number in detail. Additionally, we attempt to generalize the velocity distribution based on the obtained simulation results and reconsider the conventional steady boundary layer theory. As a result, we find that even in the laminar regime with an infinite Prandtl number, there exist regions where the simple scaling exponent Nu ∝ Ra^1/3 does not hold. Furthermore, by reconstructing the steady boundary layer theory, we resolve previous inconsistencies and formulate a more consistent expression for the Nusselt number. The findings of this study contribute to a deeper understanding of the heat transport mechanism in thermal convection with an infinite Prandtl number and to the development of theoretical frameworks in this field.