The third-order velocity structure function scaled according to Kolmogorov’s relation [see Eq. (1)] at , 400, and 700 (triangles, circles, and squares, respectively). The dashed line of slope 2 gives the small asymptote where is the velocity gradient skewness.
Scalar spectrum according to Obukhov-Corrsin scaling in DNS at and (triangles) and 1 (circles). The dashed line at 0.67 is for comparison with experiment (see Ref. 13).
Mixed velocity-scalar structure function scaled according to the Yaglom relation [see Eq. (3)] for at the same as in Fig. 1. A dashed line of slope 2 gives the small asymptote [see Eq. (12) in Ref. 12].
Skewness and flatness factors of scalar gradient component fluctuations at different . at (triangles), at (circles), and at (squares).
(Color online). Spatial distribution of the scalar dissipation rate for shown as elevated surfaces for three chosen grid planes in the simulation.
PDFs of energy dissipation rate (▵), enstrophy (◻), and scalar dissipation rate at (▴) and 1 (●) from (top) DNS at and (bottom) DNS at . All variables are normalized by the mean.
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