Probability distribution function and parallel numerical simulation in turbulence

1.我们有理论上和数值上研究的概率密度函数（PDF） Q（ξ）用于速度梯度ξ = θu/θx在被强迫的一个维度汉堡equation中，它是众所周知的，作为一个简单的模型，用于Navier-Stokes turbulence，作为一个模型，用于随机界面的增长。It is found that Q（±） is very skewed and has an algebraic tail followed by the exponential decrease for large negative ±.2。我们在名古屋大学使用高性能矢量并行机器（Fujitsu VPP 5000）和32个处理器进行了非常大的3D不压缩涡轮的DNSs。一个非常有效的FFT，用于并行机器已经开发了这个目标。在N = 1024个分辨率D13个分辨率D1时，我们找到了雷诺号R23个分辨率D2 = 490，目前的最高价值和世界记录，并找到了各种不可知的发现。results have soon been talked at the international conference on turbulence at ITP、UCSB和and attracted very strong interests of the audience （http：//online.itp.ucsb.edu/online/hydrot_c00）。3。在Navier-Stokes方程中，给出了δu（r） = u（x+r）-u（x）给我们一些洞察力到PDf Q（δu）。Q（δu）在3D稳定同源波动中的非对称形式被发现为小高斯|δu（δu）|Except prefactor and exponential for large| δu（δu）|什么是与DNS.4的好协议？我们已经通过DNS测试了压力的变化及其梯度在3D同源波动中的变化。我们发现了他们的价值观和雷诺兹的数字依赖性与古典科尔莫戈罗夫理论预测的数字不同。这种差异可以解释在泊松等式中的连续结构的术语中，在压力下。此外，还发现了压力谱的新尺度。重要的发现之一是Kolmogorov缩放中压力谱的通用常数，如4.48。

1. We have theoretically and numerically studied probability density function (PDF) Q(ξ) for the velocity gradient ξ =Ξ θu/θx in the forced one dimensional Burgers equation which is well known as a simple model for the Navier-Stokes turbulence as well as a model for the growth of random interface. It is found that Q(ξ) is very skewed and has an algebraic tail followed by the exponential decrease for large negative ξ.2. We have performed very large scale DNSs of the 3D incompressible turbulence using high performance vector parallel machine (Fujitsu VPP5000) with 32 processors at Nagoya University. A very efficient FFT for the parallel machine has been developed for this purpose. With the resolution N = 1024ィイD13ィエD1, we have attained the Raynolds number RィイD2λィエD2 = 490, the highest value and world record at present, and obtained various notable findings. The results have soon been talked at the international conference on turbulence at ITP, UCSB, and attracted very strong interests of the audience (http://online.itp.ucsb.edu/online/hydrot_c00).3. Physics or conditional averages of the dissipation term of the Navier-Stokes equation for a given value of δu(r) = u(x+r)-u(x) gives us some insights into the PDf Q(δu). Asymptotic forms of Q(δu) in 3D steady homogenous turbulence are found to be Gaussian for small |δu| except prefactor and exponential for large |δu|, which is in good agreement with DNS.4. We have examined the variances of the pressure and its gradient in the 3D homogenous turbulence by the DNS. It is found that their values and Reynolds number dependence are different from the ones predicted by classical Kolmogorov theory. The difference can be explained in terms of the coherent structure of the source term in the Poisson equation for the pressure. Also found is a new scaling for the pressure spectrum. One of the important findings is a universal constant of the pressure spectrum in the Kolmogorov scaling as 4.48.