Core dynamics of a strained vortex: instability and transition

We study the instability of a laminar vortex column (in an external orthogo nal strain field) to an axisymmetric core size perturbation, and the result ing transition to fine-scale turbulence. The perturbation, which evolves as a standing wave oscillation (i.e. core dynamics, CD), is inviscidly amplif ied by the external strain. Analysis of a weakly strained Rankine vortex ex plains the physical mechanism of instability: resonant interaction between the perturbation - the azimuthal wavenumber m = 0 wave - and m = +/-2 waves . The CD instability (CDI) - a type of elliptic instability - experiences t he fastest growth when the CD oscillation frequency equals vortex column's fluid angular velocity, such matching occurring only at specific discrete v alues of the axial wavenumber k. At this resonant frequency, the net effect of the swirl-induced tilting of perturbation vorticity and the CD-induced tilting of base flow vorticity is such that perturbation vorticity is conti nually aligned with the stretching direction of the external strain. Such s train-vorticity locking occurs for all m; hence all waves are unstable, the instability oscillation frequency being dependent on m. In a viscous Gauss ian-like vortex, CDI has low-strain, low-Re and high-k cutoffs - consequenc es of the competing effects of inviscid amplification and viscous damping. Direct numerical simulation reveals two physical-space mechanisms of transi tion: (i) formation of a thin annular vortex sheath surrounding a low-enstr ophy 'bubble' (similar to axisymmetric vortex breakdown) and the sheath's s ubsequent roll-up into smaller 'vortexlets'; and (ii) folding and reconnect ion of core vortex filaments giving rise to additional fine-grained random vorticity within the bubble -both mechanisms caused by CD-induced intense a xial flow within the vortex column. The resulting finer tubular vortices (s imilar to 'worms') have in turn their own CD, and thus this transition scen ario suggests a physical-space cascade process in developed turbulence (as well as a concomitant anti-cascade process during the bubble's collapse pha se). Additionally, we show that bending waves, in spite of their faster gro wth, effect surprisingly much slower transfer of energy into fine scales th an CDI does, and hence are less effective than CDI in vortex transition and in turbulence cascade.