Spectral analysis of temperature variances in turbulent Rayleigh-Benard convection at moderate Rayleigh numbers

Temperature variances, 〈θ'²〉, in turbulent Rayleigh-Bénard convection (RBC) are studied by direct numerical simulation (DNS) combined with spectral analyses of the budget equations. DNSs of three RBC at Rayleigh number, Ra, at 1×10⁵, 6×10⁶, and 4×10⁸ with unity Prandtl number, Pr, are used for analysis. The spectral densities of each term in the budget equation of 〈θ'²〉, namely, production, inter-scale transfer, wall-normal transport by turbulence, wall-normal transport by thermal diffusion, and dissipation, are computed as functions of length-scale, λ, and wall-normal distance, z. Scale separations between large-scale structure (LSS) and small-scale structure (SSS) are observed in both production and dissipation spectra, and the size of LSS grows with Ra. The dissipation by LSS in the near-wall region exists, but its contribution reduces with Ra. Generally, the inter-scale transfer occurs from LSS to SSS except for the small amount in the near-wall region. Also, LSS transport the 〈θ'²〉 from the outer region to the near-wall region. However, SSS transport the 〈θ'²〉 from the near-wall region to the outer region when z > δ_θ where δ_θ is the thermal boundary layer thickness. Finally, we will discuss the possibility of the universality of small-scale structures in high Ra RBC flows.