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    何建超, 方明卫, 包芸

    Scaling of Reynolds number based on maximum velocity and characteristic Reynolds number in two-dimensional thermal turbulence convection

    He Jian-Chao, Fang Ming-Wei, Bao Yun
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    • 本文计算系列二维湍流热对流, Prandtl( Pr)数和Rayleigh( Ra)数范围分别为0.25—100和1×10 7—1×10 12, 研究Reynolds( Re)数的变化规律. 以最大速度计算的 Re数与 Ra数存在标度律关系, 但中间出现间断. 研究表明, 大尺度环流形态由椭圆形到圆形的突变引起流动失稳, 导致最大速度值间断下降, 影响 Re数变化趋势的连续性. 所有 Pr数对应的流态突变特征 Re数为常值, Re c约为1.4 × 10 4, 即当 Re数达到特征 Re c时, 大尺度环流形态会发生从椭圆形到圆形的突变. 间断点对应的 Ra cPr数之间存在标度关系 Ra c -Pr 1.5. 对 Ra数进行补偿平移, 所有 Pr数的 ReRaPr –1.5的变化曲线重合, 不同 Pr数有相同的间断临界点位置, Ra c Pr –1.5= 10 9.
      Rayleigh number ( Ra) dependence in Rayleigh-Bénard (RB) convection has been studied by many investigators, but the reported power-law scaling expressions are different in these researches. Previous studies have found that when Rareaches a critical value, the flow patterns change and a transition appears in the scaling of Nu( Ra) (where Nurepresents Nusselt number) and Re( Ra) (where Redenotes Reynold number). The Grossmann-Lohse(GL) model divides the Ra-Pr(where Prrefers to Prandtl number) phase into several regions to predict the scaling expressions of Nu( Ra,Pr) and Re( Ra,Pr), indicating that the thermal dissipation behavior and kinetic dissipation behaviors are diverse in the different regions. Moreover, some physical quantities also show a transition and some structures in the flow fields, such as large scale circulation and boundary layer, change when Raincreases. In this work, we conduct a series of numerical simulations in two-dimensional RB convection with Raranging from 10 7to 10 12and Pr ranging from 0.25 to 100, which is unprecedentedly wide. The relationship between the maximum velocity and Rais investigated, and an unexpected drop happens when Rareaches a critical value Ra c, and Ra cincreases with Pr increasing. The Renumber, which is defined as a maximum velocity, also shows a plateau at Ra c. Before and after Ra c, the Rascaling exponent of Reremains 0.55, which gets smaller at very high Ra. Specially, under different Prvalues, the plateau appears at Re c≈ 1.4 × 10 4. In addition, a scaling Ra c~ Pr 1.5is found and the Rais compensated for by Pr –1.5to disscuss the relationship between Reand RaPr –1.5. It is interesting that the Re( RaPr –1.5) expressons at different Prvalues well coincide, indicating a self-similarity of Re( RaPr –1.5). The plateau appears at RaPr –1.5= 1 × 10 9, meaning that Re cwould reach 1.4 × 10 4at any Prvalue when RaPr –1.5= 1 × 10 9. To further investigate the plateau of Re, the flow patterns are compared with time-averaged velocity fields and we find that the large scale circulation (LSC) changes from ellipse to circle at Ra c. In other words, the flow pattern will change into circular LSC at Re cat different Prvalues, and Re cis a constant as mentioned above. This finding can help us to distinguish the two flow patterns with given Raand Pr, and to predict the Rescaling in an appropriate range of Rawith different Prvalues.
          通信作者:包芸,stsby@mail.sysu.edu.cn
        • 基金项目:国家自然科学基金(批准号: 11772362)资助的课题.
          Corresponding author:Bao Yun,stsby@mail.sysu.edu.cn
        • Funds:Project supported by the National Natural Science Foundation of China (Grant No. 11772362 ).
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      出版历程
      • 收稿日期:2022-02-28
      • 修回日期:2022-06-09
      • 上网日期:2022-09-16
      • 刊出日期:2022-10-05

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