A pair of counter-rotating vortices is a model flow of both practical and
fundamental significance. Such a flow may occur in the wake of aircraft
and can be hazardous to following aircraft. Knowledge of the rate of decay
of these vortices including the effects of atmospheric conditions such
as density stratification and turbulence is critical for air traffic
control. On a fundamental level, knowledge of elementary vortex flows
such as a vortex pair is a prerequisite for understanding the
interaction and behavior of vortices in more complex flows such as
In this study, the evolution of a counter-rotating vortex pair in a stably stratified fluid is investigated using direct numerical simulations. The study focuses on the short-wavelength instability occuring in this flow and subsequent decay of the vortices.
With moderately stable stratification, the instability exhibits an earlier onset and higher growth rate than in an unstratified flow. This is due to the enhanced strain that occurs when the vortices move closer together as a result of the generated baroclinic torque. The decay of the vortex pair is enhanced with stratification due to additional mechanisms that are not present in the unstratified flow. Secondary vertical vortex structures form between the primary vortices which enables exchange of fluid in the transverse direction. Detrainment of fluid from the primary vortices by the generated baroclinic torque also contributes to the breakdown of the flow.
With strong stratification, the short wavelength instability is suppressed. The strong baroclinic torque causes the primary vortices to advect towards one another, and the vortices are forced to mix which accelerates their decay. In this flow, a buoyancy time scale is comparable with a time scale of the short wavelength instability. Therefore the evolution of the vortex pair is dominated by buoyancy effects. The buoyancy oscillation leads to successive generation of baroclinic torque vorticity, resulting in oscillation of circulation at the buoyancy frequency.