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The spontaneous adjustment emission of inertia–gravity waves is investigated by examining the amount of imbalance generated during the evolution of unstable jets in an isentropic two-layer primitive equation model on the sphere. To determine the balance and thus the imbalance, potential vorticity (PV) inversion by means of the first-, second-, and third-order plain-δδ, plain-δγ, and plain-γγ balance relations, as well as the Bolin–Charney balance relations, is applied. Five sets of experiments are carried out by (i) changing the upper-layer potential temperature with a fixed initial jet speed and (ii) changing the initial jet speed with a fixed upper-layer potential temperature. For each set, the relation between the optimal measure of imbalance with the corresponding measure of balanced vortical flow is sought at the peak of instability. The minimal imbalance obtained by 1 of the above 10 PV inversion procedures is considered as the optimal.The focus herein is on the magnitude of imbalance and it...

On Imbalance Generated by Vortical Flows in a Two-Layer Spherical Boussinesq Primitive Equation Model