Assessment of Lagrangian velocity gradient models using a triple decomposition

The dynamical equation for velocity gradient evolution along Lagrangian pathlines casts nonlinear vortex stretching and strain-rate self-amplification terms in closed form. Closure models for the pressure Hessian and viscous Laplacian tensors can thus facilitate relatively inexpensive numerical modeling of small-scale turbulence via tensorial (stochastic) ODEs. Various models have been proposed over the past few decades leading to models that can reliably reproduce a number of statistical features of turbulent velocity gradients. In this study, we further interrogate the relative accuracy of existing models using a triple decomposition that splits the velocity gradient tensor into pure rotation, pure shear, and pure straining components. For example, the distinction between high vorticity regions primarily associated with pure rotation or pure shear corresponds to vortex tube-like or vortex-sheet-like flow structures, respectively. The ability of Lagrangian velocity gradient models to reproduce statistics from direct numerical simulations (DNS) provides a more discriminating test of model accuracy.