Dynamical mechanisms underlying the equilibration of absolute instability are examined in a nonlinear, quasigeostrophic, two-layer model. The key to understanding the nonlinear equilibration is in recognizing that linear absolute instabilities can be stabilized both by a reduction of the vertical shear and bu enhancement of the mean barotropic velocity. In a localized domain the equilibration process proceeds with the creation of locally convectively unstable regions downstream, which encroach onto the locally unstable regions span a minimum critical size is at least 9000 km for a wide range of parameter values chosen to investigate the midlatitude storm tracks. Fluctuations arising from local absolute instability obtain maximum amplitude in the downstream convectively unstable regions rather than in the absolutely unstable regions themselves. Together, these results suggest that if an equilibrated absolute instability were to occur in midlatitudes, a zonal band of surface easterlies exceeding 9000 km would be required and the associated enhanced variances would not be found coincident with the regions of absolute instability.

polar lows are intense subsynoptic-scale cyclones that form over high-latitude oceans in association with deep cumulus convection and strong ambient baroclinicity. Recent observations indicate that polar lows are generally initiated by a nonaxisymmetric interaction between a surface disturbance and an upper-level mobile trough. Extant theories of polar low formation preclude study of such process since they either constrain their models to be axisymmeteric, or do not explicitly account for this transient interaction. In this work the physics of interacting upper- and lower-level potential vorticity structures is studied as an initial-value problem using a three-dimensional nonlinear geostrophic momentum model that incorporates moist processes and includes strong baroclinic dynamics. Model results illustrate the rapid formation of an intense small-scale cyclone whose structure is consistent with observations of mature polar lows.

A conceptual model of polar low development is proposed. In the first stage of development, called induced self-development, a mobile upper trough initiates a rapid low-level spinup due to the enhanced omega response in a conditionally neutral baroclinic atmosphere. A secondary development follows, called diabatic destabilization, that is associated with the production of low-level potential vorticity by diabatic processes. Diabatic destabilization represents a simple mechanism for maintaining the intensity of polar low until they reach land. In exceptional cyclones in regions of sustained neutrality and surface baroclinicity.

Ideas regarding polar low equilibration and prospects for a unified theory of arctic and midlatitude cyclones are discussed.

Inclusion of Ekman damping in baroclinic models severely limits the range of unstable wavenumbers as well as the growth rate of the instabilities that remain. In contrast, there is much less reduction by the same dissipation of the transient growth of perturbations chosen to resemble those associated with observations of the initial stages of cyclogenesis. It is shown here that the Charney problem with Ekman dissipation included provides a realistic model of damped instability, that the growth rates of the unstable waves are small compared both with observed deepening rated and with deepening rated for initial value problem, and that vertical discretization is likely to produce spurious instabilities in damped models.

Development of perturbations in a baroclinic flow can arise both from exponential instability and from the transient growth of favorably configured disturbances that are not of the normal mode form. The transient growth mechanism is able to account for development of neutral and damped waves as well as for an initial growth of perturbations asymptotically dominated by unstable modes at significantly greater than their asymptotic exponential rates. Unstable modes, which are the eigenfunctions of a structure equation, are discrete and typically few in number. in contrast, disturbances favorable for transient growth from a large subset of all perturbations. To assess the potential of transient growth to account for a particular phenomena it is useful to obtain from this subset to the initial condition that gives the maximum development analogous to that of the normal modes in exponential instability theory; for instance they are the structures that the theory predicts should be found to precede rapid development.

In this work optimal perturbations for the excitation of baroclinic stable and unstable waves are found. The optima are obtained for the formation of the synoptic scale cyclones as well as for the development of planetary scale stationary and transient baroclinic Rossby waves. It is argued from these examples that optimal perturbations are likely to limit predictability on time scales relevant to the short and medium range forecast problem and that unstable modes, if present, dominate the long range forecast.

A solution of the linear initial value problem for the model of Eady with the inclusion of Ekman damping is presented. This model exhibits large transient growth of perturbations for synoptic cyclone spatial scales and a realistic value of the vertical turbulent viscosity coefficient despite the fact that all normal modes are exponentially decaying. Similar results are found for the model of Charney, implying that exponential instability cannot, in general, serve to explain the occurrence of cyclone scale disturbances in mid latitudes. Rather these are seen to arise additionally and perhaps predominantly from the release of mean slow potential energy by favorably configured initial perturbations. The Petterssen criterion  for mid latitude cyclogenesis results naturally from this development as does its extension to the formation of subtropical monsoon depressions. Implications for the maintenance of midlatitude temperature gradients are discussed.

Solution of the initial-value problem for the Eady model is presented. In the presence of boundaries, normal mode waves as well as non-modal waves exist. Energy extracted fro the mean flow during the initial development of a perturbation is found excite the the persistent normal modes. It is suggested that this process may be important to cyclogensis and in providing energy to neutral or near-neutral normal modes. In particular, the Petterssen criterion for cyclogenesis is clarified.

The asymptotic development at large time of waves arising from localized disturbances in a baroclinic flow is examined. Vertical structures unlike those associated with the more commonly examined temporal normal modes are found both for the pulse confined to a channel as previously examined and for the unconfined pulse on an infinite b-plane. These structures and their implied transports are compared to observations in the regions of storm tracks.

It is also found that the meridonal extent of the asymptotic solution becomes large compared to observed cyclone wavetrains, emphasizing the importance of flow imhomogeneity and sphericity effects in determining the latitudinal structure of eddies.

The growth of perturbations in a baoclinic flow is examined as an initial value problem. Although the long time asymptotic behavior is dominated by discrete exponentially growing normal modes when they exist, these do not form a complete set and initial intensification is shown to be dependent on the continuous spectrum. The vertical structure of perturbations emerges as an important influence on initial growth, and physically realistic disturbances are shown to grow to amplitudes where nonlinear effect are important before obtaining normal form.

Connection is made with the world of Arnol'd (1965) and Blumen (1968) and the numerical experiments of Simmons and Hoskins (1979). Application of these results to cyclogenisis in geographically fixed areas is suggested and implied constraints on numerical models discussed.

the asymptotic response of the Charney barcolinic instability problem to a localized perturbation is determined using the formalism of Briggs (1964) and exploiting a recently obtained highly accurate WKB approximate dispersion relation (Lindzen and Rosenthal, 1981). Comparison is made with previous results for two-level and Eady models.

Small scales and rapid growth characteristic of the initial stages of cyclogenisis are found and the linear dispersion relation, which can be obtained from observation of zonal wind and stability, emerges as a forecast tool for prediction of geographically local cyclogenisis.