Vorticity intensification and transition to turbulence in three-dimensional euler equations

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 firstL∞ 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.

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