## Vorticity intensification and transition to turbulence in the three- dimensional Euler equations.(English)Zbl 0755.76062

Summary: The evolution of a perturbed vortex tube is studied by means of a second- order projection method for the incompressible Euler equations. We observe, to the limits of grid resolution, a nonintegrable blowup in vorticity. The onset of the intensification is accompanied by a decay in the mean kinetic energy. Locally, the intensification is characterized by tightly curved regions of alternating-sign vorticity in a $$2n$$-pole structure. After the first $$L^ \infty$$ peak, the enstrophy and entropy continue to increase, and we observe reconnection events, continued decay of the mean kinetic energy, and the emergence of a Kolmogorov $$(k^{- 5/3})$$ range in the energy spectrum.

### MSC:

 76M20 Finite difference methods applied to problems in fluid mechanics 76F99 Turbulence 76B47 Vortex flows for incompressible inviscid fluids
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### References:

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