High resolution DNS studies of long-time behavior of homogeneous turbulent shear flow

As discussed in Isaza \& Collins [\emph{J. Fluid Mech.} {\bf 678}:14--40, 2011], the shear parameter $S^{*}$ has a pronounced effect on velocity gradient statistics for homogeneous turbulent shear flow (HTSF). Due to the importance of this effect, especially for higher $S^{*}$, we extended those studies to higher resolution using a new direct numerical simulation (DNS) code based on a pseudospectral algorithm that avoids remeshing [Brucker et al., \emph{J. Comp. Phys.} {\bf 225}:20--32, 2007], and decomposes the domain into ``pencils''. We present DNS with $2048\times 1024\times 1024$ grid points, achieving a maximum Taylor microscale Reynolds number of 300. The peak in the initial energy spectrum, viscosity, and box configuration also have been optimized to maximize the time window for well-resolved simulations (up to $S t=20$), ensuring we are well into the asymptotic regime. The DNS runs confirm the sensitivity of the large- and small-scale statistics to $S^{*}$, as was found by Isaza \& Collins. We also investigated the interaction between the fluctuating vorticity vector and rate-of-strain tensor as a function of scale, and find alignments vary dramatically, suggesting the primary source of enstrophy is at large scales, followed by a forward cascade to small scales. This helps explain the persistent sensitivity of the velocity gradient statistics to $S^{*}$. The combination of results suggests a new framework for modeling HTSF at high values of $S^{*}$.