The generation of streaks and hairpin vortices from a localized vortex disturbance embedded in unbounded uniform shear flow

Abstract

The similarity of the coherent structures (streaks and hairpin vortices) naturally occurring in different fully developed bounded turbulent shear flows as well as in transitional flows suggests the existence of a basic mechanism responsible for the formation of these structures, under various base flow conditions. The common elements for all such flows are the shear of the base flow and the presence of a localized vortical disturbance. The objective of the present numerical study is to examine the capability of a simple model of interaction, between a localized vortical disturbance and laminar uniform unbounded shear flow, to reproduce the generation mechanism and characteristics of the coherent structures that naturally occur in turbulent bounded shear flows. The effects of the disturbance ‘localized character’ in the stream-wise and spanwise directions as well as its initial orientation relative to the base flow are investigated by using several geometries of the initial disturbance. The results demonstrate that a small-amplitude initial disturbance (linear case) eventually evolves into a streaky structure independent of its initial geometry and orientation, whereas, a large-amplitude disturbance (strongly nonlinear case) evolves into a hairpin vortex (or a packet of hairpin vortices) independent of its geometry over a wide range of the initial disturbance orientations. The main nonlinear effects are: (i) self-induced motion, which results in the movement of the vortical structure relative to the base flow and the destruction of its streamwise symmetry, and (ii) the alignment of the vortical structure with the vorticity lines. This is unlike the linear case, where there is a strong deviation of the vorticity vector from the direction of the vortical structure. Qualitatively, the disturbance evolution is sufficiently independent of its initial geometry, whereas the associated quantitative characteristics, i.e. inclination angle, centre and strength (which is governed by the transient growth mechanism), strongly depend on the disturbance geometry. The Reynolds number is found to have a negligible effect on the kinematics of the vortical structure, but does have a significant effect on its transient growth. Finally, the formation of the asymmetric hairpin vortex, due to minor spanwise asymmetries of the initial disturbance, is demonstrated.