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Physical mechanism of the two-dimensional enstrophy cascade
Shiyi Chen1, Robert E Ecke, Gregory L Eyink
1Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, Maryland 21218, USA.
Physical Review Letters
|December 20, 2003
Summary
Forward enstrophy transfer in 2D turbulence needs anticorrelation between vorticity transport and gradient. Numerical simulations reveal symmetric distributions, explained by a nonlinear model, not eddy viscosity.
Area of Science:
- Fluid dynamics
- Turbulence theory
- Computational physics
Background:
- Two-dimensional turbulence exhibits forward enstrophy transfer, a key phenomenon.
- This transfer requires specific alignment between vorticity transport and gradients.
- Understanding this mechanism is crucial for turbulence modeling.
Purpose of the Study:
- To investigate the fundamental mechanism of irreversible forward enstrophy transfer in 2D turbulence.
- To analyze the relationship between vorticity transport and vorticity gradients.
- To compare numerical findings with existing theoretical approximations.
Main Methods:
- Numerical simulation of the forced Navier-Stokes equation in two dimensions.
- Calculation of probability distributions for local enstrophy flux.
- Analysis of the alignment angle between vorticity gradient and transport vector.
Main Results:
- Obtained surprisingly symmetric probability distributions for enstrophy flux and alignment angle.
- Found that vorticity transport aligns with flow streamlines, weakly with vorticity gradient.
- Demonstrated that local eddy-viscosity approximations fail to explain these results.
Conclusions:
- A local nonlinear model successfully explains the observed features of 2D turbulence.
- The physical origin of the enstrophy cascade is the steepening of vorticity gradients.
- Vorticity gradient steepening is driven by compression of vorticity level sets by large-scale strain.