Folding dynamics and its intermittency in turbulence*

Flow mixing, as already described by Reynolds in 1894, is a process that involves stretching and folding of fluid elements. In this work, by projecting the material deformation tensor onto the largest stretching direction, the dynamics of folding can be understood through the evolution of the material curvature. Results from direct numerical simulation (DNS) show that the curvature growth exhibits two regimes, first a linear stage dominated by the bending of fluid elements through a persistent velocity Hessian which then transitions to an exponential growth driven by the stretching of already strongly bent fluid elements. This transition leads to strong curvature intermittency at later stages, which can be explained by a proposed curvature-evolution model. This finding highlights the spatial inhomogeneity of mixing in turbulence and its strong history effect.