# Statistics of two-point velocity difference in high-resolution direct numerical simulations of turbulence in a periodic box

The Nature of High Reynolds Number Turbulence

Statistics of two-point velocity difference are studied by analyzing the data from high-resolution direct numerical simulations (DNS) of turbulence in a periodic box, with up to \$40963\$ grid points. The DNS consist of two series of runs; one is with \$k_{max}ta im 1\$ (Series 1) and the other is with \$k_{max}ta im 2\$ (Series 2), where \$k_{max}\$ is the maximum wavenumber and \$ta\$ the Kolmogorov length scale. The maximum, time-averaged, Taylor-microscale Reynolds number \$R_lambda\$ in Series 1 is about 1145, and it is about 680 in Series 2. Particular attention is paid to the possible Reynolds number (\$Re\$) and \$r\$ dependence of the statistics, where \$r\$ is the distance between two points. The statistics include the probability distribution functions (PDFs) of velocity differences and the longitudinal and transversal structure functions. DNS data suggest that the PDFs of the longitudinal velocity difference at different values of Re but the same values of \$r/L\$, where \$L\$ is the integral length scale, overlap well with each other when r is in the inertial subrange and when using the same method of forcing at large scales. The similar is also the case for the transversal velocity difference. The tails of the PDFs of normalized velocity differences (\$X\$’s) are well approximated by such a function as \$xp(-A|X|a)\$, where \$a\$ and \$A\$ depend on \$r\$, and where \$a\$ becomes \$pprox 1\$ in the inertial subrange. Analysis shows that the scaling exponents of the \$n\$th-order longitudinal and transversal structure functions are not sensitive to \$Re\$ but sensitive to the large-scale anisotropy and non-stationarity, and suggests that nevertheless their difference is a decreasing function of \$Re\$.

This talk is part of the Isaac Newton Institute Seminar Series series.