The analytic structure of 2D Euler flow at short times

Details The analytic structure of 2D Euler flow at short times The analytic structure of 2D Euler flow at short times

2003-10-30

arxiv.org/abs/nlin/0310044v5

Fluid Dyn. Res., 36, 221--237 (2005)

Nonlinear Sciences

Chaotic Dynamics

19 pages, 14 figures, published version

Scientific paper

10.1016/j.fluiddyn.2004.03.005

Using a very high precision spectral calculation applied to the incompressible and inviscid flow with initial condition $\psi_0(x_1, x_2) = \cos x_1+\cos 2x_2$, we find that the width $\delta(t)$ 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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