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Using direct numerical simulations of Rayleigh-B\'{e}nard 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 Prandtlnumbers in two (2D) and three (3D) dimensions. We observe close similaritiesbetween 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 adominant $k^{-2}$ spectrum. We showed that the dominant Fourier modes in the 2Dand 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.

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