The nature of balance in the atmosphere is of central importance to the dynamics of both the troposphere and the stratosphere, and unbalanced motions such as inertia-gravity waves play a significant role in many aspects of atmospheric behavior. In light of the apparent importance of upper-tropospheric jets for the generation of inertia-gravity waves in the atmosphere, this study examines the evolution of unstable barotropic jets to assess the nature and evolution of balance in these features. Specifically, numerical simulations of initially balanced zonal jets on an f plane are investigated, using a one-layer shallow-water equation model, for evidence of the breakdown of balance and the generation of inertia-gravity waves during the life cycles of the instabilities to these jets.

In these simulations, the parameters of the basic-state jet (i.e., jet width and speed) are varied systematically in an attempt to elucidate the dependence of balance on the structure and dynamical evolution of the instability. A variety of diagnostic calculations are performed to quantify the degree of imbalance present during the simulations. These calculations include evaluation of local Rossby and Froude numbers, the Lagragian Rossby number, the horizontal divergence and its time tendency, the residual of the nonlinear balance equation, and the ratio of the horizontal divergence to the relative vorticity. Results of these simulations suggest that for a broad range of basic-state jet parameters, and even in strong jets for which local Rossby and Froude numbers are not small in comparison with unity, the flow appears to remain balanced to a high degree. For the purpose of comparison, two additional sets of simulations are performed using the same basic-state jet profile: (i) simulations using the shallow-water model of initially unbalanced jets, in which large-amplitude inertia-gravity waves are excited immediately and propagate away from the jet; and (ii) simulations using a nondivergent barotropic model of unstable jets in which inertia-gravity waves are absent and the flow remains balanced for all time. The implications of these results for the nature of atmospheric balance in the vicinity of upper-tropospheric jets will be discussed, as will potential extensions to the present study. Such extensions include the examination of numerical simulations of unstable baroclinic jets using two-layer and continuously stratified primitive equation models in an attempt to investigate the nature of balance during the life cycles of unstable baroclinic waves.