Recovering isotropic statistics in turbulence simulations: the Kolmogorov 4/5th law.
One of the main benchmarks in direct numerical simulations of three-dimensional turbulence is the Kolmogorov prediction for third-order structure functions with homogeneous and isotropic statistics in the infinite Reynolds number limit. Previous direct numerical simulations (DNS) techniques to obtain isotropic statistics have relied on time-averaging structure functions in a few directions over many eddy-turnover times, using forcing schemes carefully constructed to generate isotropic data. Motivated by recent theoretical work, which removes isotropy requirements by spherically averaging the structure functions over all directions, we will present results which supplement long-time averaging by angle-averaging over up to 73 directions from a single flow snapshot. The directions are among those natural to a square computational grid, and are weighted to approximate the spherical average. We use this angle-averaging procedure to compare the statistically steady flows generated by two different forcing schemes in a periodic box. Our results show that despite the apparent differences in the two flows, their isotropic components, as measured by the Kolmogorov laws, are essentially identical. This procedure may be used to investigate the isotropic part of the small-scale statistics of any quantity of interest. The averaging process is inexpensive, and for the Kolmogorov 4/5 law, reasonable results can be obtained from a single snapshot of data. This implies consistency with the recently derived local versions of the Kolmogorov laws, which do not require long-time averages.
Taylor
Mark A
MA
Computer and Computational Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Kurien
Susan
S
Eyink
Gregory L
GL