The stationary frontal wave packet spontaneously generated in mesoscale dipoles

Three-dimensional numerical simulations of rotating, statically and inertially stable, mesoscale flows show that wave packets, with vertical velocity comparable to that of the balanced flow, can be spontaneously generated and amplified in the frontal part of translating vortical structures. These frontal wave packets remain stationary relative to the vortical structure (e.g., in the baroclinic dipole, tripole, and quadrupole) and are due to inertia-gravity oscillations, near the inertial frequency, experienced by the fluid particles as they decelerate when leaving the large speed regions. The ratio between the horizontal and vertical wavenumbers depends on the ratio between the horizontal and vertical shears of the background velocity. Theoretical solutions of plane waves with varying wavenumbers in background flow confirm these results. Using the material description of the fields it is shown that, among the particles simultaneously located in the vertical column in the dipole's center, the first ones to experience the inertia-gravity oscillations are those in the upper layer, in the region of the maximum vertical shear. The wave packet propagates afterward to the fluid particles located below.