Nonlocal nature of vortex stretching in an inviscid fluid

Abstract

Three-dimensional Euler equations are studied numerically and analytically to characterize intense vortex stretching in an inviscid fluid. Emphasis is put on the nonlocal effects stemming from the pressure term. The purpose of this paper is twofold. One is to give numerically a detailed characterization of vortex structures on the basis of previously proposed two eigenvalue problems associated with vorticity. The other is to give some mathematical analyses which highlight the role of the pressure Hessian in vortex dynamics, especially in connection with a possible singularity. Also discussed are the differences in local and global (possible) blowups. The blowup problem is not directly discussed by the present numerics at moderate resolution.