Numerical Simulations of Thermal Convection at High Prandtl Numbers

In this thesis we present the results of an extensive campaign of direct numerical simulations of Rayleigh-Bénard convection at high Prandtl numbers (10−1 ≤ Pr ≤ 104) and moderate Rayleigh numbers (105 ≤ Pr ≤ 109). The computational domain is a cylindrical cell of aspect-ratio (diameter over cell height) Γ = 1/2, with the no-slip condition imposed to the boundaries. By scaling the results, we find a 1/ Pr correction to apply to the free-fall velocity, obtaining a more appropriate representation of the large scale velocity at high Pr. We investigate the Nusselt and the Reynolds number dependence on Ra and Pr, comparing the results to previous numerical and experimental work. At high Pr the scaling behavior of the Nusselt number with respect to Ra is generally consistent with the power-law exponent 0.309. The Nusselt number is independent of Pr, even at the highest Ra simulated. The Reynolds number scales as Re ∼ √Ra/Pr, neglecting logarithmic corrections. We analyze the global and local features of viscous and thermal boundary layers and their scaling behavior wit