B-235 Burgers 乱流における速度分布の慣性相似性

概要

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One and two-point velocity distributions of the Burgers turbulence are worked out using the cross-independence hypothesis of two-point velocities, which was employed by the authors for dealing with homogeneous isotropic turbulence. One-point velocity distribution is found to be an inertial normal distribution including only the energy dissipation rate ε. Initially it starts from an uniform distribution with infinitesimal probability density, grows up as a normal distribution with decreasing variance, and eventually tends to a delta distribution corresponding to the dead still state. The kinetic energy E changes in time t as t^<-1> and the energy dissipation rate ε as t^<-2>. The velocity-sum and velocity-difference distributions are obtained as another mertial normal distribution for all finite distanceγ>0. associated with the constant ε/2 in place of ε of the one-point velocity distribution. The inertial normality makes all viscous lengths zero and causes discontinuous change of the distributions at γ=0. The inertial normality is broken for the velocity-difference distribution at the inertial range, which is obtained numerically as an asymmetric non-normal distribution.
日本流体力学会の論文
2003-07-28