Singularities in cascade models of the Euler equation |
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Authors: | C. Uhlig J. Eggers |
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Affiliation: | 110. Fachbereich Physik, Universit?t - Gesamthochschule - Essen, D-45117, Essen, Germany
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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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