Barotropic And Baroclinic Instability Of Rossby Waves On The Infinite Beta-Plane

The normal mode instability problem for a stationary Rossby wave of finite amplitude and arbitrary orientation in a two-level model with zonal mean shear in the vertical is examined on the infinite beta-plane using a Floquet technique. The results are compared to the instability of a finite amplitude stationary Rossby wave in a barotropic model. The instability of the barotropic model linearized about the upper level flow of the stationary two-level Rossby wave is also examined; forcing must be introduced to the barotropic equations in this case to balance the time tendency of the basic state. The instabilities of the three models are compared in an attempt to address two questions. First, are the barotropic instabilities related to any of the two-level model instabilities? Second, what are the consequences of introducing forcing in the stability problem? It is found that the barotropic models accurately reproduce those instabilities of the two-level model that have a nearly barotropic structure; these are not necessarily low-frequency instabilities. The introduction of forcing is found to have a significant impact on the barotropic instabilities. Special emphasis is placed on parameter ranges judged to be analogous to the mid-latitude atmosphere. Possible relevance of the results to geophysical flows and the instability problem on the sphere are discussed.