A second-order theory of baroclinic waves is developed to investigate non-quasi-geostrophic behavior in disturbances in which latent heat release associated with condensation is permitted to occur in an atmosphere saturated with water vapor. A two-level formulation without β-effect is used to analyze these disturbances. The analysis involves an expansion of the flow into a basic state zonal flow with superimposed perturbation which is assumed to be independent of the meridional direction. The superimposed perturbation consists of linear combination of a quasi-geostrophic contribution and a non-quasi-geostrophic departure. The basic state flow with the superimposed quasi-geostrophic perturbation has been investigated by the authors in a previous paper. The governing equations for the non-quasi-geostrophic contribution consist of a nonlinear (thermodynamic) integro-differential equation and a nonhomogenous (vorticity) differential equation. The nonlinearity is a direct result of latent heat release associated with pseudo-adiabatic assent; i.e., saturated ascending air parcels and dry descending air parcels. The nonhomogeneity arises from the non-quasi-geostrophic terms in the vorticity equation. In this theory we use the quasi-geostrophic contribution to calculate the non-quasi-geostrophic terms which generate the second-order solution.
The problem is characterized by two parameters, namely a rotational Froude number F = 2f2(SdP22kd2)−l (where f is the Coriolis parameter, Sd the static stability in descending portion of the wave, p2 the pressure at the middle level, and kd = π/b, b being the horizontal extent of the descending or dry portion of the wave) and a moisture parameter ε which is proportional to the midlevel vertical gradient of mean flow specific humidity. For ε ≠ 0 the disturbances are characterized by a/b ≠ 1, where a is the horizontal extent of the ascending or wet portion of the wave. The quasi-geostrophic contribution to the disturbance is characterized by two modes for F > 1. The first mode has a narrow region of strong ascending motion and a wide region of weak descending motion (a/b < 1), with the reverse for the second mode (a/b > 1). Thew solutions, developed by the authors in an earlier paper, are used to calculate the non-quasi-geostrophic solution terms mentioned above.
For the first moist mode, due to the non-quasi-geostrophic effects, both the trough and ridge are intensified at the upper level with stronger intensification of the trough and are weakened at the lower level with considerable weakening of the ridge. The formation of the frontal zone on the east side of the descending region is a feature similar to that in the dry model with non-quasi-geostrophic effects. For the second moist mode, due to the non-quasi-geostrophic effects, both trough and ridge are weakened at the upper level, but they am intensified at the lower level. The temperature profile in each region is nearly symmetric. The total vertical motion field is asymmetric in each region for both the first and second moist modes.
The main characteristics of the energetics are described by the transports due to the first-order eddy. The transports due to the second-order eddy have only minor influence except for large F such as F ≥ 10 for the first mode and except for ε near unity for the second mode.