Public-database enabled analysis of Lagrangian dynamics of isotropic turbulence near the Vieillefosse tail

We study the Lagrangian time evolution of velocity gradient dynamics near the Vieillefosse tail. The data are obtained from fluid particle tracking through the $1024^4$ space-time DNS of forced isotropic turbulence at $Re_{\lambda}=433$, using a web-based public database (http://turbulence.pha.jhu.edu). Examination of individual time-series of velocity gradient invariants $R$ and $Q$ show that they are punctuated by strong peaks of negative $Q$ and positive $R$. Most of these occur very close to the Viellefosse tail along $Q = - (3/2^{2/3}) R^{2/3}$. It is found there that the magnitude of pressure Hessian has positive Lagrangian time-derivative, meaning that it increases in order to resist the rapid growth. We also observe a ``phase delay'' of the pressure Hessian signals compared to those of $R$ and $Q$, indicative of an ``overshoot'' of the controlling mechanism. We also examine the trajectories in the recently proposed 3-D extension of the $R-Q$ plane (see L\"{u}thi B, Holzner M, Tsinober A. 2009, J. Fluid Mech. {\bf 641}, 497-507). Finally, Lagrangian models of the velocity gradient tensor are examined in the same light to identify similarities and differences with the observed dynamics. Such comparisons supply informative guidance to model improvements.