The analytic structure of 2D Euler flow at short times

T. Matsumoto; J. Bec; U. Frisch

doi:10.1016/j.fluiddyn.2004.03.005

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arXiv · nlin/0310044

The analytic structure of 2D Euler flow at short times

T. Matsumoto·J. Bec·U. Frisch

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Abstract

Using a very high precision spectral calculation applied to the incompressible and inviscid flow with initial condition $ψ_0(x_1, x_2) = \cos x_1+\cos 2x_2$, we find that the width $δ(t)$ of its analyticity strip follows a $\ln(1/t)$ law at short times over eight decades. The asymptotic equation governing the structure of spatial complex-space singularities at short times (Frisch, Matsumoto and Bec 2003, J.Stat.Phys. 113, 761--781) is solved by a high-precision expansion method. Strong numerical evidence is obtained that singularities have infinite vorticity and lie on a complex manifold which is constructed explicitly as an envelope of analyticity disks.

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T. Matsumoto, J. Bec, U. Frisch. 2005-06-01. The analytic structure of 2D Euler flow at short times. https://doi.org/10.1016/j.fluiddyn.2004.03.005

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