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We analyze 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–Bénard convection (ACRBC) for Rayleigh number Ra ∈[108,1011], Prandtl number Pr = 10.7, and inverse Rossby number 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 Ra=1011, it is found that BO59-like scaling Eu(kr)∼kr−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 vs the order coincide with the theoretical prediction of BO59 scaling ζ u p =3p/5 basically. The second-order temperature SFs exhibit a gradual transition from the Obukhov–Corrsin behavior at scales smaller than the Bolgiano scales to the BO59 behavior at scales larger than the Bolgiano scales. The slopes from the third to sixth-order temperature SFs are similar, which is similar to classical Rayleigh–Bénard convection and Rayleigh–Taylor turbulence. The probability density functions (p.d.f.) of temperature fluctuations δT/σT 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.

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Tangram is one of the oldest puzzle games in China. It can make up volatile and wonderful patterns. To master the game, it would be ideal if the players can go through several complexity levels from the easiest to the most complicated. However, tangram today does not have the difficulty grade. Only a similar puzzle game—Japanese jigsaw puzzle has the difficulty grade which is not very reasonable. And the grading process is not provided. Therefore, we try to provide the theoretical basis of dividing the difficulty grades by means of probability of the patterns. We hope we can make some complements to this ancient game. Among the complicated influential factors, we sum up three key elements: the number of answers，the length of side, the basic figures. Based on these points, we have devised three plans, the procedural thinking of computer, the length-of-side principle, division principle, to calculate the probability. Then, we made comprehensive analysis on the probability. Finally, we got the difficulty grade of some classical tangram patterns. Moreover, we summarize some skills of piecing together the patterns.