The stability of continuous baroclinic models with planetary vorticity gradient

Abstract

The linearized continuous baroclinic model of Eady with planetary vorticity gradient is studied by considering a normal mode disturbance. The problem is reduced to a confluent hypergeometric equation with proper boundary conditions. The stability of this problem is expressed in terms of the behavior of an analytical function. A proof is given to show the existence of neutral waves. Fjörtoft's advective model with planetary vorticity gradient is obtained by letting the static stability vanish in Eady's model with planetary vorticity gradient. A comparison of the two models shows that they are very similar. Static stability leads to a lower level of non-divergence than in the pure advective case. An expansion technique is used to study the deviation near the advective model. Although this method is useful only for medium-scale unstable waves, it gives a simple formula for the phase speed and growth rate.