Vorticity dynamics in a breaking internal gravity wave. Part 2. Vortex interactions and transition to turbulence

Abstract

A companion paper (Part 1) employed a three-dimensional numerical simulation to examine the vorticity dynamics of the initial instabilities of a breaking internal gravity wave in a stratified, sheared, compressible fluid. The present paper describes the vorticity dynamics that drive this flow to smaller-scale, increasingly isotropic motions at later times. Following the initial formation of discrete and intertwined vortex loops, the most important interactions are the self-interactions of single vortex tubes and the mutual interactions of multiple vortex tubes in close proximity. The initial formation of vortex tubes from the roll-up of localized vortex sheets gives the vortex tubes axial variations with both axisymmetric and azimuthal-wavenumber-2 components. The axisymmetric variations excite axisymmetric twist waves or Kelvin vortex waves which propagate along the tubes, drive axial flows, deplete the tubes' cores, and fragment the tubes. The azimuthal-wavenumber-2 variations excite m=2 twist waves on the vortex tubes, which undergo strong amplification and unravel single vortex tubes into pairs of intertwined helical tubes; the vortex tubes then burst or fragment. Reconnection often occurs among the remnants of such vortex fragmentation. A common mutual interaction is that of orthogonal vortex tubes, which causes mutual stretching and leads to long-lived structures. Such an interaction also sometimes creates an m=1 twist wave having an approximately steady helical form as well as a preferred sense of helicity. Interactions among parallel vortex tubes are less common, but include vortex pairing. Finally, the intensification and roll-up of weaker vortex sheets into new tubes occurs throughout the evolution. All of these vortex interactions result in a rapid cascade of energy and enstrophy toward smaller scales of motion.