Vorticity gradient stretching in the direct enstrophy transfer process of two-dimensional turbulence

Zeyou Zhou, Lei Fang, Nicholas T. Ouellette, and Haitao Xu
Phys. Rev. Fluids 5, 054602 – Published 11 May 2020

Abstract

Vortex gradient stretching is believed to be the mechanism that generates large vorticity gradients at small scales and consequently maintains the enstrophy cascade to small scales in two-dimensional turbulence. In this work, using particle tracking measurements of two-dimensional turbulence in a soap-film flow, we show experimental evidence that in the direct enstrophy cascade range, the vorticity gradient is preferentially perpendicular to the instantaneous stretching direction. We also show that in regions where the stretching direction and the vorticity gradient are perpendicular to each other, the enstrophy flux is on average from large to small scales, while it is from small to large scales in other regions. Moreover, when observing the angle between stretching and the vorticity gradient in a coordinate system following a fluid particle trajectory, i.e., in the Lagrangian view, we observe that the vorticity gradient direction responds to but lags behind the stretching direction. Therefore, we observe a stronger alignment between the vorticity gradient direction with the stretching direction at an earlier time. At all scales in the direct cascade range, the evolution of the angle between the vorticity gradient and the stretching direction displays a time scale given by the mean enstrophy, independent of the scale, providing direct experimental support for the theoretical argument that vorticity is nearly constant in the direct cascade range.

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  • Received 21 November 2019
  • Accepted 8 April 2020

DOI:https://doi.org/10.1103/PhysRevFluids.5.054602

©2020 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Zeyou Zhou

  • Center for Combustion Energy, Tsinghua University, Beijing 100084, China and Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China

Lei Fang and Nicholas T. Ouellette

  • Department of Civil and Environmental Engineering, Stanford University, Stanford, California 94305, USA

Haitao Xu*

  • Center for Combustion Energy, Tsinghua University, Beijing 100084, China and School of Aerospace Engineering, Tsinghua University, Beijing 100084, China

  • *hxu@tsinghua.edu.cn

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Vol. 5, Iss. 5 — May 2020

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