  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.

Chaotic Dynamics