ORIGINS AND EVOLUTION OF IMBALANCE IN SYNOPTIC-SCALE BAROCLINIC WAVE LIFE-CYCLES

A set of balance equations is derived that is appropriate for analysis of the three-dimensional anelastic system and is based on expansions in Rossby and Froude number similar to those employed in the study of the shallow-water equations by Spall and McWilliams. Terms that consti tute the usual balance equations are formally retained here in additio n to non-Boussinesq terms of the same order arising from the vertical variation of the background density field. The authors apply the deriv ed set of equations diagnostically to the analysis of three-dimensiona l, anelastic numerical simulations of a synoptic-scale baroclinic wave . Of particular interest in this analysis is the degree to which and t he time at which the flow becomes appreciably unbalanced, as well as t he form of the imbalance itself. Unbalanced motions are here defined a s departures from solutions of the balance equations. Application of t his analysis procedure allows us to identify two classes of unbalanced motion, respectively: 1) unbalanced motion that is slaved to the bala nced motion and is therefore characterized by the same time and length scales as the balanced motion (i.e., higher-order corrections on the ''slow'' manifold) and 2) unbalanced motion that is on a faster timesc ale than the large-scale balanced motion but is nevertheless forced by these same balanced motions (e.g., forced internal gravity waves). It will be shown in the analysis that both forms of imbalance arise in t he frontal zones generated during the numerical simulation, but that t he gravity wave generation is probably a numerical artifact of insuffi cient vertical resolution as the slope of the surface front decreases below the threshold required for consistent horizontal and vertical re solution. The total unbalanced motion field is dominated by the slower advective motion, but the numerically generated gravity waves neverth eless reach a peak amplitude comparable to that of the slower unbalanc ed motion. Whether internal wave radiation would persist, or perhaps b ecome more intense, with increased spatial resolution is an issue that is left unresolved in the present analysis.