Scale-dependent enstrophy production rates in a turbulent boundary layer

Coarse-graining is indispensable for extracting a hierarchy of vortices in fully developed turbulent flow with multiscale nature. In the present study, for a high-Reynolds-number turbulent boundary layer, we employ two simple coarse-graining methods in real space; namely, a Gaussian filter and the combination of the Gaussian filters at two scales. The former corresponds to a low-pass filter of Fourier modes, while the latter corresponds to a band-pass filter. We also examine two different filter widths for the band-pass filter. Then, we show difference in the statistics of the three filtered fields. Since the velocity gradients in turbulence are mainly determined by the smallest-scale motions, vortical structures identified by the second invariant Q of the velocity gradient coarse-grained by the filters are similar. However, there is difference between low- and band-pass filtered fields in the contribution to the enstrophy production rates. This is because the production rates are determined not only by the magnitude of the strain rates but also by the alignment between the vorticity and the stretching direction. In addition, since vortices are not created in the entire system, the conditional sampling by the value of Q is essential to understand the generation mechanism of the hierarchy of vortices. The conditional analysis of the band-pass filtered fields demonstrates that small-scale vortices in the log layer are stretched by twice-larger vortices, whereas they weaken the twice-larger vortices. This observation is consistent with the picture of the energy cascade. We also show that when using the band-pass filter, these conclusions are robust irrespective of the choice of the filter width.