The analytic structure of 2D Euler flow at short times

Abstract

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.

19 pages, 14 figures, published version

References in corpus (1)

• Lagrangian singularities of steady two-dimensional flow

Cited by in corpus (8)

• Singularity formation for Prandtl's equations
• Numerical study of shock formation in the dispersionless Kadomtsev-Petviashvili equation and dispersive regularizations
• Nature of complex singularities for the 2D Euler equation
• Numerical Study of the semiclassical limit of the Davey-Stewartson II equations
• Analysis of complex singularities in high-Reynolds-number Navier-Stokes solutions
• Complex-space singularities of 2D Euler flow in Lagrangian coordinates
• On complex singularities of the 2D Euler equation at short times
• Analytic structure of solutions of the one-dimensional Burgers equation with modified dissipation