Euler-alpha and vortex blob regularization of vortex filament and vortex sheet motion

Abstract

The Euler-alpha and the vortex blob model are two different regularizations of incom- pressible ideal fluid flow. Here, a regularization is a smoothing operation which controls the fluid velocity in a stronger norm than $L^2$ . The Euler-alpha model is the inviscid version of the Lagrangian averaged Navier–Stokes-alpha turbulence model. The vortex blob model was introduced to regularize vortex flows. This paper presents both models within one general framework, and compares the results when applied to planar and axisymmetric vortex filaments and sheets. By certain measures, the Euler-alpha model is closer to the unregularized flow than the vortex blob model. The differences that result in circular vortex filament motion, vortex sheet linear stability properties, and core dynamics of spiral vortex sheet roll-up are discussed.