Dynamics of the tetrad-based velocity gradient in turbulent flows

We investigate the structure and evolution of turbulent flows with the help of the perceived velocity-gradient, determined from four fluid particles initially forming a regular tetrad of size $r_0$. The main feature of the turbulent dynamics can be conveniently captured by a reduced description, in terms of two invariants of the velocity gradient. When $r_0$ is in the inertial range of scales, the evolution of averaged quantities can be parametrized by two dimensionless parameters, which vary slowly with $r_0$. We also characterize the fluctuations around the conditional mean, which represent the dynamics at scales below $r_0$. Using data from both Lagrangian particle tracking experiments and DNS, we show that the behavior qualitatively follows some earlier theoretical prediction, but with interesting new features.