Daigen Fukayama

Velocity field statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulation

Velocity field statistics in the inertial to dissipation range of three-dimensional homogeneous steady turbulent flow are studied using a high-resolution DNS with up to N=10243 grid points. The range of the Taylor microscale Reynolds number is between 38 and 460. Isotropy at the small scales of motion is well satisfied from half the integral scale (L) down to the Kolmogorov scale (η). The Kolmogorov constant is 1.64±0.04, which is close to experimentally determined values. The third order moment of the longitudinal velocity difference scales as the separation distance r, and its coefficient is close to 4/5. A clear inertial range is observed for moments of the velocity difference up to the tenth order, between 2λ≈100η and L/2≈300η, where λ is the Taylor microscale. The scaling exponents are measured directly from the structure functions; the transverse scaling exponents are smaller than the longitudinal exponents when the order is greater than four. The crossover length of the longitudinal velocity struct...

Longitudinal Structure Functions in Decaying and Forced Turbulence

In order to reliably compute the longitudinal structure functions in decaying and forced turbulence, local isotropy is examined with the aid of the isotropic expression of the incompressible condit...

Stretched lognormal distribution and extended self-similarity in 3D turbulence

Using data of a direct numerical simulation (DNS) of 3D turbulence it is shown that the moments of order between 1 and 6 of both longitudinal and transverse components of velocity increment for forced as well as decay turbulence can be described by stretched lognormal distribution for all scales from the dissipation to the inertial ranges and for all values of Reynolds number investigated in this DNS (50< R λ <459). A new (local) version of extended self-similarity has been used for this purpose. Effects of vortex structure on increment of velocity field in forced and in decay turbulence are briefly discussed.

Probability Density Function of Longitudinal Velocity Increment

In this paper we present an analysis of the PDF for the longitudinal velocity increment with the aid of the conditional average method (CAM). The functional forms of the necessary averages are derived and compared with the results of simulation. The derived PDF is categorically shown; the Gaussian for small amplitudes, the stretched exponential for intermediate ones and the exponential for large ones. The comparison with the PDF obtained in high Reynolds number flows is given.