Baroclinic Instability in an Euler Equations–Based Column Model: The Coexistence of a Deep Synoptic-Scale Mode and Shallow Subsynoptic-Scale Modes

Abstract

The authors provide a detailed analysis of a shallow mode of subsynoptic-scale baroclinic instability by analyzing a one-dimensional column model in which the assumption of balance is applied to the basic-state flow but in which nongeostrophic unbalanced effects are retained in the description of the evolution of the perturbation under the Boussinesq approximation. This model is employed to analyze the stability of a meridionally confined mean state that is based upon hydrodynamic fields extracted from the central columns of a tropospheric cross section of the midlatitude jet stream. Numerical solutions are obtained at very high resolution through application of a sparse matrix method for solution of the corresponding cubic eigenvalue problem. Thereby the existence of a deep synoptic-scale mode and boundary-confined subsynoptic-scale modes is confirmed. The spatial scale and phase speed of these modes agree with those previously obtained on the basis of both nonseparable stability analysis and solution of the associated initial value problem in the companion paper by Yamazaki and Peltier. Both one-dimensional and nonseparable shallow modes share the property that they are characterized by the presence of an inertial critical layer, and the lack of a short-wave cutoff of the subsynoptic-scale modes suggested by analyses of the nonseparable models is more clearly shown in the column model. However, the growth rate of the shallow mode in the column model is approximately 1 order of magnitude smaller than those of the structures delivered by the nonseparable analyses, and the vertical structure and the energy budget of these modes vary dramatically depending on the sign of the meridional wavenumber that determines the direction of meridional propagation.