Irreversibility and small-scale generation in 3-dimensional turbulent flows

In 3-dimensional turbulent flows, the irreversibility of turbulence manifests itself by an asymmetry of the probability distribution of the instantaneous power p of the forces acting on fluid elements: the third moment of p was found to be negative. Here, I will discuss the relation between this negative third moment and vortex stretching, which is traditionally related to the generation of small scales. The construction is based on a decomposition of the power p as a sum of a local contribution, due to the variation of velocity at a fixed point in space, plus a convective part, due to the displacement of particles in the flow. The third moment of the latter term, which dominates the statistics, is explicitly expressed in terms of vortex stretching,