A Numerical Study of the Three-Dimensional Structure and Energetics of Unstable Disturbances in Zonal Currents: Part I

Abstract

The dynamic instability properties and the structure and energetics of unstable disturbances in both pure baroclinic and pure barotropic zonal currents are investigated by applying an eigenvalue technique to the finite-difference version of a linear quasi-geostrophic model. Numerical results are compared with well-known theoretical results. Their accuracy is also examined by varying the number of subdivisions. It is found that the numerical method gives sufficiently accurate results, particularly in describing the structure and energetics of the primary, unstable, cyclone-scale disturbances. In the baroclinic case, the unstable waves produce northward and upward transports of sensible heat. These conversion rates are pronounced in the lower layer. The short waves are characterized as shallow waves, the long waves as upper waves. The symmetric perturbations in the barotropic cosine-jet current are unstable for intermediate wavelengths, while the antisymmetric perturbations are stable. The barotropic parabolic-jet current is also stable for symmetric perturbations. The results for vertically higher resolution in the barotropic case show that there exist internal modes in addition to the nondivergent mode, due to the stratification of the basic atmosphere. The unstable perturbations grow at the expense of the zonal kinetic energy and tend to transform an initial single-jet into a double-jet current as a result of the meridional convergence of the Reynold stresses. The first internal mode is confined to the stratosphere and converts eddy kinetic energy to eddy available potential energy.