Eigenvalue problems in three-dimensional Euler flows

Abstract

A simple analysis shows that there are two eigenvalue problems associated with vorticity. Dynamically, the vorticity tends to be a simultaneous eigenvector of the rate-of-strain tensor S and the pressure hessian P at the point of maximum enstrophy, as shown in the numerical simulations. This suggests that intense vortex stretching occurs at particular fluid particles. Indeed, high vorticity regions are more localized in Lagrangian marker space than in physical space. It is also shown that the P alignment holds valid even kinematically for random fields.