Spectra and structure functions of the temperature and velocity fields in supergravitational thermal turbulence

Abstract

We analyse the power spectra and structure functions (SFs) of the temperature and radial velocity fields, calculated in the radial and azimuthal directions, in annular centrifugal Rayleigh-B\'{e}nard convection (ACRBC) for Rayleigh number Ra $ \in [{10^8},{10^{11}}]$, Prandtl number Pr = 10.7, and inverse Rossby number $\rm{Ro}^{-1} = 16$ using the spatial data obtained by quasi-two-dimensional direct numerical simulation. Bolgiano and Obukhov-like (BO59-like) scalings for the energy spectrum in both the azimuthal and radial directions and thermal spectrum in the azimuthal direction are observed. The range of BO59-like scaling becomes wider as Ra increases. At $\rm{Ra} = 10^{11}$, it is found that BO59-like scaling ${E_u}({k_r}) \sim {k_r}^{ - 11/5}$ spans nearly two decades for the energy spectrum calculated in the radial direction. Power-law fittings in the range larger than the Bolgiano scales, the scaling exponents of transverse and longitudinal velocity SFs versus the order coincide with the theoretical prediction of BO59 scaling $\zeta _p^u = 3p/5$ basically. The second-order temperature SFs exhibit a gradual transition from the Obukhov-Corrsin behaviour at scales smaller than the Bolgiano scales to the BO59 behaviour at scales larger than the Bolgiano scales. The slopes from the 3rd to 6th-order temperature SFs are similar, which is similar to classical Rayleigh-B\'{e}nard convection and Rayleigh-Taylor turbulence. The probability density functions (p.d.f.) of temperature fluctuations $\delta T/{\sigma _T}$ reveal the cold plumes are strong and the p.d.f. in different regions at high Ra are similar. The stronger turbulent-mixing and larger centrifugal buoyancy in ACRBC may result in the BO59-like scaling.

From sheared annular centrifugal Rayleigh–Bénard convection to radially heated Taylor–Couette flow: exploring the impact of buoyancy and shear on heat transfer and flow structure

“…(2007) and Wang et al. (2022 b ), if we assume , then the exact relation of our system is where is the mean energy dissipation rate, is the mean energy dissipation rate of the laminar and non-vortical flow, is the quasi-Prandtl number, and is a correction factor. In Regime I, , we have .…”

“…Derived from the kinetic energy balance equation, the exact relation represents the energy balance between buoyant energy injection, shear energy injection and mechanical dissipation. In the dimensional form, referring to derivation from Eckhardt et al (2007) and Wang et al (2022b), if we assume αθ(Ω c + u ϕ /r) 2 ru r V,t = CαΩ 2 c ru r θ V,t , then the exact relation of our system is…”

“…2020, 2022; Wang et al. 2022 b ), is taken for water at , and is set to be . Considering the Boussinesq approximation, is required.…”

“…In the present study, we consider the coupling effect of shear and buoyancy on the flow structure and heat and momentum transfer, that is, (Nu h , Nu ω ) = f (Ra, Ω). Therefore, referring to the results of our previous experiments and simulations of ACRBC (Jiang et al 2020(Jiang et al , 2022Wang et al 2022b), Pr = 4.3 is taken for water at 40 • C, and η is set to be 0.5. Considering the Boussinesq approximation, αΔ 1 is required.…”