Compressible turbulent convection at very high Rayleigh numbers

2024/11/15 by Tiwari, Harshit, Lekha Sharma, Sharma, Lekha +2 · 2 citations
Engineering · #Fluid Dynamics and Turbulent Flows #Computational Fluid Dynamics and Aerodynamics

paper · pdf · doi:10.48550/arxiv.2411.10372

Abstract

Heat transport in highly turbulent convection is not well understood. In this paper, we simulate compressible convection in a box of aspect ratio 4 using computationally-efficient MacCormack-TVD finite difference method on single and multi-GPUs, and reach very high Rayleigh number (Ra) -- 10¹⁵ in two dimensions and 10¹¹ in three dimensions. We show that the Nusselt number Nu ∝ Ra^0.3 (classical scaling) that differs strongly from the ultimate-regime scaling, which is Nu ∝ Ra^1/2. The bulk temperature drops adiabatically along the vertical even for high Ra, which is in contrast to the constant bulk temperature in Rayleigh-Bénard convection (RBC). Unlike RBC, the density decreases with height. In addition, the vertical pressure-gradient (-dp/dz) nearly matches the buoyancy term (ρg). But, the difference, -dp/dz-ρg, is equal to the nonlinear term that leads to Reynolds number Re ∝ Ra^1/2.

Cited by

• Thermal convection in 1, 2, 3 and 4 dimensions
• Plane-layer Rayleigh-Bénard convection up to Ra=10¹¹: Near-wall fluctuations and role of initial conditions

Related

• Classical 1/3 Nusselt number scaling in highly turbulent compressible convection
• Scalings of heat transport and energy spectra of turbulent Rayleigh-Benard convection in a large-aspect-ratio box
• Scaling of high-Rayleigh-number convection based on internal convective boundary layer
• Turbulent convection at very high Rayleigh numbers and the weakly nonlinear theory
• Deciphering boundary layer dynamics in high-Rayleigh-number convection using 3360 GPUs and a high-scaling in-situ workflow