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

Abstract

The multiple modes of dynamic instability and their three-dimensional structure and energetics for various zonal currents containing both vertical and horizontal shears are investigated through use of a linear quasi-geostrophic model, as a continuation of the previous paper. Numerical results are obtained from the complete set of complex eigenvalues and eigenvectors of the finite-difference version of the governing equations. For jet-type zonal currents containing absolute vorticity extrema at various latitudes, there exist two primary modes of instability, each corresponding to a unique category of zonal available energy sources. The first is mainly characterized by baroclinic processes (modified by horizontal shear) and the other by barotropic mechanisms (modified by vertical shear). The baroclinic mode dominates for shorter waves, while the barotropic mode dominates for longer waves. The baroclinic mode increases the kinetic energy of the zonal current; conversely, the barotropic mode decreases the zonal kinetic energy. The presence of both energy sources tends to reduce individual rates of energy conversions. However, the baroclinic instability mechanism dominates in the lower layer, while the barotropic instability is most pronounced near the tropopause, particularly for longer waves. Zonal currents which are similar but contain no active pure barotropic instability mechanism are found to possess only one strongly unstable mode which withdraws potential energy from the zonal flow, yet feeds kinetic energy into the jet.