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Characterization of large scale quantities and energy spectrum for very large Prandtl numbers

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We investigate the scaling of the Nusselt and Péclet number as well as that of energy spectrum using direct numerical simulation for very large and ∞ Prandtl numbers. Simulations have been performed in a box for the Rayleigh numbers in the range 10^4 − 10^8 and for the Prandtl numbers 10^2, 10^3, and ∞. Nusselt number increases with the Rayleigh number as Nu ∼ Raγ with γ in the range 0.29 − 0.33. Péclet number scales as Pe ∼ Raζ with ζ in the range 0.57 − 0.61. The observed results are in general agreement with earlier results. The energy spectrum for Pr = ∞ neither follow the Kolmogorov-Obukhov nor the Bolgiano-Obukhov scaling.

Author(s):

Ambrish Pandey    
Department of Physics, Indian Institute of Technology Kanpur
India

Mahendra Kumar Verma    
Department of Physics, Indian Institute of Technology Kanpur
India