The Evolution of Finite-Amplitude Localized Vortices in Homogeneous Shear

Abstract

Recently we have shown that the interaction of a localized vortical disturbance and the shear of the external base flow is responsible for the generation of counter rotating vortex pair and hairpin vortices (that are frequently observed in turbulent shear flows). In this paper we consider the evolution of finite-amplitude localized vortical disturbances in shear flows. Due to their localization in space, the surrounding base flow is assumed to have homogeneous shear to leading order. An analytical-based method is developed enabling to numerically solve the governing equations in a novel way in Fourier space with Lagrangian co-ordinates. When possible the new results are compared with previous ones.