Mishra Pankaj Kumar, Verma Mahendra K
Department of Physics, Indian Institute of Technology, Kanpur 208 016, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 May;81(5 Pt 2):056316. doi: 10.1103/PhysRevE.81.056316. Epub 2010 May 19.
We compute the spectra and fluxes of the velocity and temperature fields in Rayleigh-Bénard convection in turbulent regime for a wide range of Prandtl numbers using pseudospectral simulations on 512(3) grids. Our spectral and flux results support the Kolmogorov-Obukhov (KO) scaling for zero Prandtl number and low Prandtl number (P=0.02) convection. The KO scaling for the velocity field in zero-Prandtl number and low-Prandtl number convection is because of the weak buoyancy in the inertial range (buoyancy is active only at the very low wave numbers). We also observe that for intermediate Prandtl numbers (P=0.2) the KO scaling fits better with the numerical results than the Bolgiano-Obukhov (BO) scaling. For large Prandtl number (P=6.8) , the spectra and flux results are somewhat inconclusive on the validity of the KO or BO scaling, yet the BO scaling is preferred over the KO scaling for these cases. The numerical results for P=1 is rather inconclusive.
我们使用512(3)网格上的伪谱模拟，计算了在广泛的普朗特数范围内，湍流状态下瑞利-贝纳德对流中速度场和温度场的谱和通量。我们的谱和通量结果支持零普朗特数和低普朗特数（P = 0.02）对流的柯尔莫哥洛夫-奥布霍夫（KO）标度。零普朗特数和低普朗特数对流中速度场的KO标度是由于惯性范围内浮力较弱（浮力仅在非常低的波数下起作用）。我们还观察到，对于中等普朗特数（P = 0.2），KO标度比博尔贾诺-奥布霍夫（BO）标度更符合数值结果。对于大普朗特数（P = 6.8），谱和通量结果对于KO或BO标度的有效性有些不确定，但在这些情况下，BO标度比KO标度更可取。P = 1的数值结果相当不确定。
