Model Coherent Structure Dynamics: Vortex Reconnection, Core Dynamics and Interaction with Turbulence

Abstract

Direct numerical simulations of the Navier-Stokes equations for three idealized vortex interactions are analyzed to obtain insights into the dynamics of coherent structures in turbulent flows. We first study the vortex reconnection mechanism which presumably is important in cascade and mixing in turbulent flows. The dynamical significance of axial flow in coherent structures inferred from this interaction is explored further by studying the evolution of an axisymmetric laminar vortex tube with nonuniform core. Evolution of vorticity wavepackets in such a vortex tube is first explained as a coupling between swirl and meridional flow. We show how this evolution is better understood by the motion of polarized vorticity components, obtained via complex helical wave decomposition of the vorticity and velocity fields. Finally, by treating such a vortex tube as a prototypical segment of a coherent structure we study its interaction with background, fine-scale, isotropic turbulence. This study shows polarization and organization of small scales by the coherent structure, and subsequent feedback on the structure from the small scales, thus providing the mechanism for a direct coupling between large and fine scales in turbulent flows.