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.
- Received 21 November 2019
- Accepted 8 April 2020
DOI:https://doi.org/10.1103/PhysRevFluids.5.054602
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