主催: 日本学術会議 機械工学委員会・土木工学・建築学委員会 合同IUTAM分科会
共催: 日本機械学会, 日本気象学会, 日本地震工学会, 日本物理学会, 農業農村工学会, 応用物理学会, 化学工学会, 地盤工学会, 土木学会, 日本応用数理学会, 日本風工学会, 日本計算工学会, 日本建築学会, 日本原子力学会, 日本航空宇宙学会, 日本材料学会, 日本数学会, 日本船舶海洋工学会, 日本伝熱学会, 日本流体力学会, 日本レオロジー学会
Statistical theories of turbulence developed so far dealing with the mean velocity products of various orders are outlined historically and reformulated as the non-equilibrium statistical mechanics of fluid turbulence based on the Lundgren-Monin equations for the multi-point velocity distributions and the cross-independence closure hypothesis proposed by Tatsumi. According to this formalism, the infinite set of the Lundgren-Monin equations is closed as the finite set of equations for the n-point velocity distributions f(n) (n>=1) , the minimum deterministic set of which being composed of the oneand two-point velocity distributions f and f(2), the latter being represented by the velocity-sum distribution g+ and the velocity-difference distribution g-. As an outstanding result, it is shown that the energy-dissipation rate of turbulence e is expressed in terms of the distribution g- which is mostly contributed from small-scale turbulence, making clear analogy with the "fluctuation-dissipation theorem" of non-equilibrium statistical mechanics. Another remarkable result is the exactness of the present closure in the sense that the closed terms of the Lundgren-Monin equations are exactly equivalent with the unclosed terms of the same equations. This property of the closure is confirmed by the fact that the moment equations derived from the closed equations for the velocity distribution are precisely equivalent with the corresponding equations for the mean velocity products derived from the Navier-Stokes equation directly.
