The vorticity dynamics of instability and turbulence in a breaking internal gravity wave
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences. 1999
Received: 24 July 1998
Accepted: 20 December 1998
Published: 26 June 2014
We perform a three-dimensional simulation of a breaking internal gravity wave in a stratified, compressible, and sheared fluid to investigate the vorticity dynamics accompanying the transition from laminar to turbulent flow. Baroclinic sources contribute preferentially to eddy vorticity generation during the initial convective instability of the wave field, yielding counter-rotating vortices aligned with the external shear flow. These vortices enhance the spanwise vorticity of the shear flow via stretching and distort the spanwise vorticity via advective tilting. The resulting vortex sheets undergo a dynamical (Kelvin-Helmholtz) instability which rolls the vortex sheets into tubes which link, in turn, with the original streamwise convective rolls to produce a collection of intertwined vortex loops. Following the formation of discrete vortex loops, the most important interactions are the self-interactions of single vortex tubes and the mutual interactions of adjacent vortex tubes in close proximity. The initial formation of vortex tubes from the roll-up of localized vortex sheets imposes axial vorticity variations having both axisymmetric and azimuthal wavenumber two components. Axisymmetric variations excite axisymmetric twist waves, or Kelvin vortex waves, which propagate along the tubes, drive axial flows, and deplete and fragment the tubes. Azimuthal wavenumber two variations excite m = 2 twist waves on the vortex tubes which amplify and unravel single vortex tubes into pairs of intertwined helical tubes. Other interactions, judged less fundamental to the turbulence cascade, include reconnection among tube fragments, mutual stretching of orthogonal tubes in close proximity, excitation of azimuthal wavenumber one twist waves, and the continual roll-up of weaker vortex sheets throughout the evolution. Collectively, these vortex interactions result in a rapid cascade of energy and enstrophy toward smaller scales of motion.