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 so...