@techreport{oai:jaxa.repo.nii.ac.jp:00043592,
 author = {巽, 友正 and 吉村, 卓弘 and Tatsumi, T. and Yoshimura, T.},
 month = {Jun},
 note = {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 in an incompressible viscous fluid. 1) Since no external excitation has been introduced, turbulence decays in time, and the self-similar evolution of the statistical characteristics is assumed.  One-point velocity distribution is found to be an inertial normal distribution including only the energy dissipation rate ε as the inverse diffusion parameter. Initially it starts from an uniform distribution with infinitesimal probability density, grows up in time as a normal distribution with decreasing variance, and eventually tends to a delta distribution corresponding to the dead still state. During this decay process, the kinetic energy E changes in time t as E ∝ t^(-1) and thus the energy dissipation rate ε as ε ∝ t^(-2) .  Two-point velocity distribution is expressed in terms of the velocity-sum and velocity-difference distributions. The both distributions are obtained as another inertial normal distribution for all finite distance r > 0, associated with the constant ε/2 in place of ε of the one-point velocity distribution.  The inertial normality of the both distributions makes all length-scale related with the viscosity ν vanishingly small and causes discontinuous change of the distributions in the limit of small distance r -> 0. The inertial normality is broken for the velocity-difference distribution at the inertial range, which is obtained numerically as the asymmetric non-normal distribution depicted in Fig.2. Except for this case, the prevailing inertial normality of the general statistics of the Burgers turbulence provides us with a bright prospect for the extension of the theory to more complex turbulent flows., 資料番号: NALSP0059020, レポート番号: NAL SP-59},
 title = {Burgers乱流における速度分布の慣性相似性},
 year = {2003}
}