Similarities between 2D and 3D convection for large Prandtl number

Abstract

Using direct numerical simulations of Rayleigh-Bénard convection (RBC), we perform a comparative study of the spectra and fluxes of energy and entropy, and the scaling of large-scale quantities for large and infinite Prandtl numbers in two (2D) and three (3D) dimensions. We observe close similarities between the 2D and 3D RBC, in particular the kinetic energy spectrum $E_u(k)\sim k^{-13/3}$, and the entropy spectrum exhibits a dual branch with a dominant $k^{-2}$ spectrum. We showed that the dominant Fourier modes in the 2D and 3D flows are very close. Consequently, the 3D RBC is quasi two-dimensional, which is the reason for the similarities between the 2D and 3D RBC for large- and infinite Prandtl numbers.

9 pages, 13 figures

References in corpus (4)

• Comparison between two and three dimensional Rayleigh-Bénard convection
• Flow reversals in turbulent convection via vortex reconnections
• Benchmarking and scaling studies of a pseudospectral code Tarang for turbulence simulations
• Scaling of heat flux and energy spectrum for "very large" Prandtl number convection

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• On the Applicability of Low-Dimensional Models for Convective Flow Reversals at Extreme Prandtl Numbers
• Non-Boussinesq convection at low Prandtl numbers relevant to the Sun
• Lagrangian coherent sets in turbulent Rayleigh-Bénard convection
• Reversals in infinite-Prandtl-number Rayleigh-Bénard convection
• Similarities between the structure functions of thermal convection and hydrodynamic turbulence
• Transient and steady convection in two dimensions