The dynamics of balance in upper-tropospheric jets and fronts are examined through idealized numerical simulations of baroclinic-wave life cycles in a two-layer primitive equation (PE) model. The primary goal of this investigation is to identify the characteristic conditions for which jets that are initially in balance evolve towards an unbalanced state and generate inertia-gravity waves, and the physical mechanisms responsible for this behavior. The basic-state zonal jet is varied systematically in these simulations to examine the dependence of the evolution of balance both on the initial parameters of the jet (i.e., Rossby and Froude numbers based on jet width and speed) and on the evolution of the unstable baroclinic wave and its accompanying jets and fronts. The present study represents the first step in a hierarchical investigation of the dynamics of balance in baroclinic-wave life cycles. Although highly idealized, the two-layer PE model is the simplest model that can incorporate both baroclinic waves and inertia-gravity waves, and thus provides an ideal framework in which to identify the relevant parameter regimes and characteristic flow signatures for which balance may be expected to break down. The results of these simulations may then be used as a reference point for simulations in more general dynamical frameworks (e.g., continuously stratified PE model with a stratosphere) to explore these regimes and signatures in more detail by allowing the incorporation of realistic vertical structure and gravity wave propagation.

The parameters of the basic-state jet control the structure and growth rate of the baroclinic wave, which in turn impact significantly on the nature of balance as measured by traditional diagnostic calculations (e.g., based on the nonlinear balance system). Results of these simulations indicate that the degree of imbalance so measured is highly dependent on the growth rate of the baroclinic wave, and hence on the time scale of evolution of the developing jet maximum in addition to its maximum speed. For rapidly growing waves, in the vicinity of the jet maximum local Rossby numbers are significantly larger than unity, local Froude numbers are of order unity, and the horizontal divergence and its tendency become locally large, suggesting that the evolution of this feature may not be well described by balanced dynamics. Moreover, the location of this apparent imbalance is consistent with that described in previous investigations of inertia-gravity wave generation by upper-tropospheric jets and fronts. Nevertheless, the ratio of horizontal divergence to relative vorticity remains significantly smaller than unity throughout these simulations; hence, the possibility exists that the structure and evolution of these rapidly evolving jets may be well described by higher-order balanced systems. To explore this possibility, additional diagnostic calculations, including potential vorticity inversion systems, are being developed and will be applied to the simulations in an attempt to quantify more accurately the degree of imbalance associated with the simulated jets. Results from these calculations will be presented, as will further discussion of the limitations of the two-layer PE model and the extension of the present study to incorporate simulations in more general dynamical frameworks as discussed above.