New Approaches to Vortex Dynamics: Core Dynamics, Helical Waves, and Interaction with Fine Scale Turbulence

Abstract

Some new aspects of vortex dynamics, coherent structures and interaction with fine-scale turbulence are reviewed. In the absence of any appropriate measurement technology for the 3-D instantaneous vorticity field we rely on direct numerical simulation of the Navier-Stokes equations using spectral methods in an 1283 periodic cube. Recognizing from our study of the vortex reconnection mechanism that vortex lines associated with coherent structures are frequently helical, we study first the evolution of a laminar vortex column with a nonuniform core at a Reynolds number Re≡Γ/v=665, and then the vortex’s evolution in the presence of fine-scale homogeneous, isotropic turbulence. We show that core dynamics, ignored so far, can be very significant in vortex dynamics and vortex interactions and consists of travelling vorticity wave packets along the vortex axis. We also show that core dynamics can be better explained by complex helical wave decomposition — a new mathematical tool — than in terms of coupling between swirl and meridional flow. Our results reveal a new mechanism of direct coupling between coherent structures and fine-scale turbulence and hence the failure of the hypothesis of local isotropy. The fine scales are energized by the coherent vortex at the latter’s boundary and evolve into larger scale spiral structures through pairing and become polarized. When these structures become sufficiently strong, they induce bending waves on the vortex, thus guaranteeing their continued survival.KeywordsCoherent StructureVortex RingVortical StructureVortex LineVortex TubeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.