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Folding Dynamics and Its Intermittency in Turbulence.

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Fluid element folding in turbulence is depicted by material curvature evolution. This study reveals two growth regimes and a transition, offering new insights into turbulent energy cascade and mixing.

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Area of Science:

  • Fluid dynamics
  • Turbulence research
  • Nonlinear dynamics

Background:

  • Turbulent flows involve complex deformation of fluid elements through stretching and folding.
  • Understanding these dynamics is crucial for comprehending energy cascade and mixing processes.

Purpose of the Study:

  • To investigate the dynamics of fluid element folding in turbulence.
  • To characterize the evolution of material curvature during turbulent deformation.
  • To link the velocity Hessian to the folding process for a deeper understanding of turbulence.

Main Methods:

  • Direct numerical simulations (DNS) were employed to model turbulent flows.
  • The material deformation tensor was projected onto the largest stretching direction.
  • The evolution of material curvature was analyzed to understand folding dynamics.

Main Results:

  • Curvature growth was observed to follow two distinct regimes: a linear stage and an exponential-growth stage.
  • A transition between these regimes was identified, driven by the stretching of already bent fluid elements.
  • Strong curvature intermittency was observed at later stages, explained by a proposed curvature-evolution model.

Conclusions:

  • The study provides a new perspective on fluid element folding in turbulence by analyzing material curvature.
  • The link between velocity Hessian and folding offers novel insights into energy cascade and mixing mechanisms.
  • The findings extend beyond classical linear descriptions of stretching dynamics in turbulent flows.