Potential vorticity and inertia-gravity waves

23 pages, 9 figures, 3 appendixThe dynamics of balanced and wave flow components is investigated using the theoretical structure of potential vorticity (PV) and a vector potential φ = (φ, ψ, φ) under the isochoric (volume-preserving), Boussinesq, and f-plane approximations. The vector potential φ = (φ, ψ, φ) defines both the three-dimensional velocity (proportional to the curl of φ) and the density anomaly (proportional to the divergence of φ). The vertical potential φ is obtained through PV inversion from the three-dimensional (3D) PV field and the horizontal potential φ h = (φ, ψ). As a first example of this approach, it is shown that the dipole wave packet spontaneously generated in rotating and stably stratified dipolar flows has a clear signal in the vertical potential φ diagnosed from this kind of PV inversion. It is also shown that the wave packet, despite departing from a plane inertia-gravity wave solution, does not significantly contribute to the PV field (i.e. it has zero PV). A new interpretation of φ is introduced. It is proved that the Laplacian of φ may be dynamically interpreted, using the divergence equation, as the buoyancy force and Coriolis acceleration contributions to the difference between the amounts of 3D stretching and vorticity. It is also found that the use of zero PV inversion in high-order dynamics (inertia-gravity wave permitting dynamics) is useful to set up inertia-gravity wave fields satisfying required boundary conditions. The combined use of PV inversion and vector potential φ enables a simple way by which a vortical flow can be put into correspondence with a wave field which has initially some similarities with the vortical flow. Finally, it is suggested that a good candidate for a wave quantity could be the vertical component of the isopycnal vector ω a × ▽ ρ, where ω a is the absolute vorticity and ρ is mass density. The pattern of this component is very consistent with that of the dipole wave packet at different vertical levels. © 2011 Copyright Taylor and Francis Group, LLC.Peer Reviewe