Influence of an elliptic instability on the merging of a co-rotating vortex pair

Abstract

We study the nonlinear evolution of the elliptic instability and its influence on the merging process of two corotating Batchelor vortices using a spectral DNS approach. First, we analyse the nonlinear saturation of the elliptic instability for a single strained vortex, with and without axial jet, for moderate Reynolds numbers (Re= Gamma/nu approx= 12500, where Gamma is the circulation and nu the kinematic viscosity). We show that the vortex deformation induced by the instability remains limited to the vortex core region. The second part of our work focuses on the influence of the elliptic instability on the merging process. We compare three cases : no instability (2D), elliptic instability without axial jet, and elliptic instability with axial jet, the latter case being relevant to aircraft wakes. Qualitative and quantitative differences between the three different cases are pointed out and discussed in the context of aircraft vortices.