Suppression of vorticity in vortex and pipe flow interactions

Abstract

The interaction of a vortex and a pipe flow, modelled as the Lamb–Oseen vortex and the Poiseuille flow, respectively, is investigated by means of stability analyses and direct numerical simulations (DNS). From the distribution of the most unstable mode, it is observed that the instability is induced by the combination of the radial gradients of the base azimuthal and axial velocity components, e.g. an axial (or azimuthal) vorticity perturbation acts on the axial (or azimuthal) base velocity via a lift-up effect to generate axial (or azimuthal) velocity streaks, which are further stretched by the base azimuthal (or axial) velocity to create azimuthal (or axial) vorticity. This lift-up-stretch mechanism is confirmed in DNS of the model base flow initially perturbed by the most unstable mode. After nonlinear saturation, the perturbations decay since the flow no longer supports instability after sufficient radial mixing induced by the lift-up of the azimuthal and axial velocity components. These observations suggest that the vorticity outside the vortex core can be suppressed by instabilities if a streamwise boundary layer flow exists outside the core.