Localized Disturbances and Their Relation to Turbulent Shear Flows

Abstract

The resemblance among coherent structures naturally occurring in fully developed bounded turbulent shear flows, transitional flows and free shear layers suggests the existence of a basic single mechanism responsible for the formation of the structures under various base flow conditions. The common elements in all such flows are the shear of the base flow and the presence of a localized vortical disturbance within this shear. The objective of the present study is to examine the capability of a simple model of interaction between a localized vortical disturbance and the surrounding ‘simple’ laminar shear flow where the velocity vector is (at most) a linear function of the coordinates, to reproduce the generation mechanism and characteristics of the coherent structures that naturally occur in turbulent bounded shear flows (counter-rotating vortex pairs and hairpin vortices) and free shear layers (‘rib vortices’). The research combines numerical, experimental and theoretical approaches. Numerically, we follow the evolution of a localized vortical disturbance in an unbounded pure shear flow. The results demonstrate that a small amplitude initial disturbance eventually evolves into a streaky structure independent of its initial geometry and orientation, whereas, a large amplitude disturbance evolves into a hairpin vortex. The main nonlinear eect is the self-induced motion, which results in the movement of the vortical structure relative to the base flow. Experimentally, 2D flow visualization and a Holographic Particle Image Velocimetry (HPIV) system are employed to study the evolution of coherent structures artificially generated in a plane Poiseuille air flow. The 2D visualization demonstrates (in accordance with the CFD results) that a small amplitude disturbance evolves into a counter-rotating vortex pair, and if the amplitude is suciently large a train of hairpin vortices is formed. The HPIV method is utilized to obtain the instantaneous topology of the hairpin vortex and its associated 3D distributions of the two (streamwise and spanwise) velocity components as well as the corresponding wall-normal vorticity. The quantitative distribution of the latter (when properly scaled) agrees well with the CFD results, further supporting our above mentioned view of a basic universal mechanism. Finally, the generation of an intensified counter-rotating vortex pair from a localized vortex disturbance in plane stagnation flow is studied theoretically, following the temporal evolution of its fluid impulse. Good agreement with complementary CFD results is obtained.