Singularities in cascade models of the Euler equation

Details Singularities in cascade models of the Euler equation Singularities in cascade models of the Euler equation

1996-12-19

arxiv.org/abs/chao-dyn/9612025v1

Nonlinear Sciences

Chaotic Dynamics

33 pages (REVTeX) including eps-figures, Stylefile here.sty

Scientific paper

10.1007/s002570050337

The formation of singularities in the three-dimensional Euler equation is investigated. This is done by restricting the number of Fourier modes to a set which allows only for local interactions in wave number space. Starting from an initial large-scale energy distribution, the energy rushes towards smaller scales, forming a universal front independent of initial conditions. The front results in a singularity of the vorticity in finite time, and has scaling form as function of the time difference from the singularity. Using a simplified model, we compute the values of the exponents and the shape of the front analytically. The results are in good agreement with numerical simulations.

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