  Modeling the velocity gradient tensor A along Lagrangian trajectories in
turbulent flow requires closures for the pressure Hessian and viscous Laplacian
of A. Based on an Eulerian-Lagrangian change of variables and the so-called
Recent Fluid Deformation closure, such models were proposed recently. The
resulting stochastic model was shown to reproduce many geometric and anomalous
scaling properties of turbulence. In this work, direct comparisons between
model predictions and Direct Numerical Simulation (DNS) data are presented.
First, statistical properties of A are described using conditional averages of
strain skewness, enstrophy production, energy transfer and vorticity
alignments, conditioned upon invariants of A. These conditionally averaged
quantities are found to be described accurately by the stochastic model. More
detailed comparisons that focus directly on the terms being modeled in the
closures are also presented. Specifically, conditional statistics associated
with the pressure Hessian and the viscous Laplacian are measured from the model
and are compared with DNS. Good agreement is found in strain-dominated regions.
However, some features of the pressure Hessian linked to rotation dominated
regions are not reproduced accurately by the model. Geometric properties such
as vorticity alignment with respect to principal axes of the pressure Hessian
are mostly predicted well. In particular, the model predicts that an
eigenvector of the rate-of-strain will be also an eigenvector of the pressure
Hessian, in accord to basic properties of the Euler equations. The analysis
identifies under what conditions the Eulerian-Lagrangian change of variables
with the Recent Fluid Deformation closure works well, and in which flow regimes
it requires further improvements.
