The vorticity dynamics of instability and turbulence in a breaking internal gravity wave

Abstract

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.

Vertical propagation, breaking and effects of nonlinear gravity waves in the atmosphere

“…They simulated propagation of waves in a rectangle atmospheric region with horizontal and vertical dimensions of 120 and 48 km, respectively. Other authors (Fritts and Garten, 1996;Andreassen et al, 1998;Fritts et al, 1999) simulated the effect of atmospheric internal wave breaking due to Kelvin-Helmholtz instabilities. Their models are three-dimensional ones and wave propagation and breaking was simulated in rectangle regions with horizontal and vertical extensions of 4H Â 2H and 4H, respectively, where H is the scale height.…”

Large-scale dynamical influence of a gravity wave generated over the Antarctic Peninsula – regional modelling and budget analysis

“…However, these PV anomalies could also result from vorticity dynamics involving baroclinic vorticity generation within the convectively unstable phase of the wave followed by vortex tilting and stretching (e.g. Fritts et al 1999), since these source terms in the absolute vorticity equation are implicitly contained in the advection term of the PV equation. Therefore, Fig.…”

“…It was then shown that these convective overturning regions were associated with shedding streamwise counter vortices that eventually played a role in the large-scale dynamical influence of the simulated AP gravity wave (e.g. Fritts et al, 1999;Chen et al, 2007).…”

“…Three-dimensional dynamics associated with gravity wave breaking in a non-rotating atmosphere has been addressed by Fritts et al (1999) in a dimensionless idealised case study of a gravity wave propagating and convectively overturning in a three-dimensional geophysical flow characteristic of the middle atmosphere. These authors were particularly interested in the vorticity dynamics accompanying the transition from laminar to turbulent flow and obtained that streamwise counter-rotating vortices developed through baroclinic vorticity generation within the convectively unstable phase of the wave.…”

A factor involved in efficient breakdown of supersonic streamwise vortices

“…Moet et al 16 showed that local changes in the vortex core radius are linked to instability and vortex bursting in subsonic flows. Fritts et al 17 pointed out the importance of interactions between vortical structures on compressible breakdown from a topological perspective. As shown in Fig.…”