Project/Area Number  09640260 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  Nagoya Institute of Technology 
Principal Investigator 
GOTOH Toshiyuki Nagoya Inst. of Tech., Dep. of Systems Eng., A. Prof., 生産システム工学科, 助教授 (70162154)

CoInvestigator(Kenkyūbuntansha) 
KOWADA Tadashi Nagoya Inst. of Tech., Dep. of Systems Eng.,. Prof., 生産システム工学科, 教授 (80015875)
YAMADA Hideo Nagoya Inst. of Tech., Dep. of Systems Eng., Prof., 生産システム工学科, 教授 (50021605)
中野 徹 中央大学, 理工学部・物理学科, 教授 (50055224)
NAKANO Tohru Chuo Univ. Dep. of Phys. Prof. (50050224)

Project Fiscal Year 
1997 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥3,100,000 (Direct Cost : ¥3,100,000)
Fiscal Year 1999 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1998 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1997 : ¥2,100,000 (Direct Cost : ¥2,100,000)

Keywords  turbulence / DNS / Burgers / spectrum / parallel machine / FFT / pressure / Probability density function / 乱流 / 確率密度関数 / 並列 / 圧力 / バーガース乱流 / スペクトル / 並列化 / 確率分布関数 / 並列計算 
Research Abstract 
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 NavierStokes 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 NavierStokes 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.
