Folding dynamics and its intermittency in turbulence

TL;DR

This paper investigates the folding dynamics in turbulence by analyzing the evolution of material curvature, revealing a transition from linear to exponential growth regimes and highlighting the role of curvature intermittency in energy cascade and mixing.

Contribution

It introduces a curvature-evolution model linking velocity Hessian to folding, offering new insights into turbulence dynamics beyond classical linear theories.

Findings

Curvature growth shows two regimes: linear followed by exponential.

Transition to exponential growth causes curvature intermittency.

Velocity Hessian is crucial in understanding energy cascade and mixing.

Abstract

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.