The analytic structure of 2D Euler flow at short times

Using a very high precision spectral calculation applied to the incompressible and inviscid flow with initial condition ψ0(x1, x2) = cos x1 + cos 2x2, 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.