Turbulent flow in the bulk of Rayleigh–Bénard convection: small-scale properties in a cubic cell

Abstract The Rayleigh number (Ra) scaling of the global Bolgiano length scale L₁, ₆₋₎₁₀₋ and the local Bolgiano length scale L₁, ₂₄₍ₓₑ₄ in the centre region of turbulent Rayleigh–Bénard convection are investigated for Prandtl numbers Pr= 0. 7 and 4. 38 and 3 10^5 Ra 3 10^9. It is found that L₁, ₂₄₍ₓₑ₄ does not necessarily exhibit the same scaling as L₁, ₆₋₎₁₀₋. While L₁, ₆₋₎₁₀₋ is monotonically deceasing as L₁, ₆₋₎₁₀₋ Ra^- 0. 10 for both Pr, L₁, ₂₄₍ₓₑ₄ shows a steep increase beyond a certain Ra value. The complex scaling of the local Bolgiano length scale in the centre is a result of the different behaviour of the temperature-variance dissipation rate, ₓ, and the turbulent-kinetic-energy dissipation rate, ₔ. This shows that for sufficiently high Ra the flow is well-mixed and hence temperature is passively advected. It is also observed that the Ra -range in which L₁, ₂₄₍ₓₑ₄ exhibits the same scaling as the global Bolgiano length scale is increasing with increasing Pr. It is further observed that for Pr= 4. 38 and Ra 3 10^7 the local vertical heat flux in the centre region is balanced by the turbulent-kinetic-energy dissipation rate. For higher Ra we find that the local heat flux is decreasing. At Pr= 0. 7 we do not observe such a balance, as the measured heat flux is between the heat fluxes estimated through the turbulent-kinetic-energy dissipation rate and the temperature-variance dissipation rate. We therefore suggest that the balance of the local heat flux might be Prandtl-number dependent. The conditional average of the local vertical heat flux Nu { ₔ, ₓ }₂₄₍ₓₑ₄ in the core region of the flow reveals that the highest vertical heat flux occurs for rare events with very high dissipation rates, while the joint most probable dissipation rates are associated with very low values of vertical heat flux. It is also observed that high values of ₔ and ₓ tend to occur together. It is further observed that the longitudinal velocity structure functions approach Kolmogorov K41 scaling. The temperature structure functions appear to approach Bolgiano–Obukhov BO59 scaling for r L₁, ₂₄₍ₓₑ₄, while a scaling exponent smaller than the BO59 scaling is observed for separations r L₁, ₂₄₍ₓₑ₄. The mixed velocity and temperature structure function for <jats: inline-graphic xmlns: xlink="