Singularities in cascade models of the Euler equation

C. Uhlig; J. Eggers

doi:10.1007/s002570050337

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arXiv · chao-dyn/9612025

Singularities in cascade models of the Euler equation

C. Uhlig·J. Eggers

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Abstract

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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C. Uhlig, J. Eggers. 1996-12-19. Singularities in cascade models of the Euler equation. https://doi.org/10.1007/s002570050337

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