Statistical properties of the local structure are investigated using the data of direct numerical simulation of homogeneous isotropic turbulence for Reλ = 60.1 ~ 287.6 and turbulent channel flows for Reτ = 180, 400, 800, and 1270. The dimensionless second invariant is used as the representative local structure, and is defined as the second invariant of a velocity gradient tensor normalized by the magnitude of the velocity gradient tensor. In homogeneous isotropic turbulence, the probability density function (pdf) profiles of the dimensionless second invariant show good agreement for different values of Reynolds number. The volume fraction, the average, and the variance of the dimensionless second invariant converge to certain values at high Reynolds number, respectively. For the turbulent channel flows, the pdf profiles of the dimensionless second invariant for different values of Reynolds number coincide very well for the distance from the wall in wall units. The probability density and the volume fraction of the dimensionless second invariant at the center of the channel are in good agreement with those of homogeneous isotropic turbulence.
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