Barotropic Instability with Downstream and Asymmetric Cross-Stream Variations: Idealized Calculations

The barotropic instability of basic states with downstream and asymmetric cross-stream variations is investigated using the linearized, non-divergent barotropic vorticity equation in a periodic beta channel. A single expression for streamfunction defines the basic state; the variations are introduced by parameter changes. Eigenvalue and time integration methods are employed to determine the instabilities. When downstream variation is present, the maximum amplitude of the unstable streamfunction is always located downstream from the location of maximum latitudinal shear. This occurs because the disturbance propagates through a range of longitudes where the flow is locally barotropically unstable. The instability is sensitive to the degree of downstream variation. When there is strong variation there is more concentration of streamfunction amplitude in the regions downstream of the jet maximum, smaller disturbance scales and smaller growth rates than when the flow is more parallel. The smaller grow...