  Fluid elements deform in turbulence by stretching and folding. In this work,
by projecting the material deformation tensor onto the largest stretching
direction, the dynamics of folding is depicted 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
folding 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. The link between velocity Hessian to folding
provides a new way to understand the crucial steps in energy cascade and mixing
in turbulence beyond the classical linear description.
