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The origin of the stationary frontal wave packet spontaneously generated in rotating stratified vortex dipoles

The origin of the stationary frontal wave packet spontaneously generated in rotating and stably stratified vortex dipoles is investigated through high-resolution three-dimensional numerical simulations of non-hydrostatic volume-preserving flow under the f-plane and Boussinesq approximations. The wave packet is rendered better at mid-depths using ageostrophic quantities like the vertical velocity or the vertical shear of the ageostrophic vertical vorticity. The analysis of the origin of vertical velocity anomalies in shallow layers using the generalized omega-equation reveals that these anomalies are related to the material rate of change of the ageostrophic differential vorticity, which in shallow layers are themselves related to the large-scale ageostrophic flow along the dipole axis, and in particular, to the advective acceleration. It is found that on the anticyclonic side of the dipole axis the combined effect of the speed and centripetal accelerations causes an anticyclonic rotation of the horizontal ageostrophic vorticity vector in a time scale of about one inertial period. These facts support the hypothesis that the origin of the stationary and spontaneously generated frontal wave packet at mid-depths is the large acceleration of the fluid particles as they move along the anticyclonic side of the dipole axis in shallow layers.