Analysis and evolution of balance in unstable barotropic jets

The nature of balance in the atmosphere is of central importance to the dynamics of both the troposphere and the stratosphere, with unbalanced motions such as inertia-gravity waves playing a significant role in many aspects of atmospheric behavior. In light of the importance of upper-tropospheric jets for the generation of inertia-gravity waves, this study examines unstable barotropic jets to assess the nature and evolution of balance in these features.

This issue is explored using the simplest non-trivial dynamical framework in which balanced and unbalanced flows can coexist, namely the one-layer shallow-water equations. Initially balanced, zonal, barotropic jets (Bickley jet profile) on an f-plane are investigated for evidence of the breakdown of balance and the generation of inertia-gravity waves during the unstable life cycles of these jets. Parameters of the basic-state jet (i.e., jet width and speed) are varied systematically (resulting in a range of Rossby and Froude numbers) in an attempt to elucidate the balance dependence on the structure and evolution of the instability in the jet region. A second-order potential vorticity inversion scheme is utilized to obtain balanced and unbalanced dynamic variable fields in each simulation.

For strong jets, neither the Rossby number nor the Froude number is small compared to unity; therefore, the applicability of traditionally scale analysis is unclear (i.e., the balance condition is no longer valid and a breakdown of balance should occur). In contrast, the results of the potential vorticity inversion reveal that nonlinear balance is essentially valid for the Bickley jet profile, even though Rossby and Froude numbers are O(1) for strong jets.