Abstract
The probability distributions of the various quantities characterizing three-dimensional turbulence are investigated. The numerical simulation of the turbulence we study here has been conducted to study decaying homogeneous turbulence at moderately large Reynolds numbers by Yamamoto and Hosokawa. Various turbulent fields are constructed from the velocity Fourier modes contained in three different regions of the wave-number space: inertial range, dissipation range and whole wave-number space. As a result, nearly Gaussian and near-exponential distributions are obtained for the velocity, its longitudinal and lateral derivatives in the physical space and the Fourier modes in the wave-number space. They mostly confirm the result of She et al.. The near-exponential distributions are obtained not only for the velocity derivative fields, but also for the velocity field obtained from the dissipation range. It is found that the asymmetric distributions of the longitudinal derivative, which is closely related to the stretching of fluctuating vorticity in the turbulent flow, are detected for all the fields. The flatness factors of higher longitudinal derivatives of the velocity are also evaluated in addition to the skewness factor of the first longitudinal derivative.