Lagrange identification of absolutely unstable regimes in wake

Abstract

A novel approach to identify the absolute and convective character of instabilities is presented. The employed vortex blob method is found to be well suited to reproduce the dynamics of unstable wavepackets. The prediction of the classical local, linear stability analysis, according to which the wavepacket in an absolutely unstable flow contains upstream travelling modes, was confirmed accurately by the simulations. The non-linearity of the employed method enable the tracking of the disturbance waves up into the highly non-linear regime. The analysis is for a parallel shear flow but it is easily extended to non-parallel flows as well. The method may be combined with a vorticity generation mechanism to model the no-slip boundary condition and therefore to simulate flows past body-surfaces.