Role of Large-Scale Forcing on Velocity Gradient Dynamics in Turbulence

This work highlights the profound role of forcing in small-scale velocity-gradient (VG) dynamics.  Specifically, we seek to explain the interactions among forcing, inertial, pressure, and viscous effects leading to the observed small-scale behavior. Data from direct numerical simulations of isotropic and anisotropic incompressible turbulence is used to examine the effect of forcing on the evolution of VG invariants, Q and R. It is demonstrated that forcing, opposes inertial and viscous action in the strain-dominated nodal topologies and it counteracts the non-local pressure in rotation-dominated unstable focal topologies. The most important contribution of forcing is to balance the dilatational probability current of the combined inertial-pressure-viscous action. To a significant extent, the solenoidal probability current of inertial-pressure-viscous action, drives the overall VG dynamics. These findings have important implications in the development of stochastic VG models.