The development characteristics of quasi-geostrophic baroclinic disturbances

Abstract

An overall qualitative analysis is made for the development characteristics of quasi-geostrophic pure baroclinic disturbances by using both integral properties and the WKB method. The results obtained by these two methods are consistent, but the WKB method yields more conclusions.

The sufficient condition for stability and the necessary condition for instability are investigated. A local individual disturbance can be unstable only if it is located in the layer where the instability criteria is satisfied locally. For an arbitrarily given initial condition, the instability might be first realized locally, and then spread into adjacent levels.

More attention is paid to the problems of development. A disturbance is called developing (decaying) if its energy increases (decreases). In a vertical shear zonal flow, all characteristics of a disturbance, such as total wave length, vertical wave length, orientation of axis (trough-ridge line), amplitude and energy usually change with time during the evolutional process. The development of a disturbance depends only on the orientation of its axis and its location related to the basic current. A developing (decaying) disturbance enlarges (shortens) its total wave length and vertical wave length, and gradually turns its axis more vertically (more tilted). If the meridional gradient of zonal mean potential vorticity is every where positive during the period of growth (decay), the maximum amplitude of the disturbance moves toward (out from) the jet and is accompanied by a vertical energy flux toward (out from) the jet. In the unstable case, the energy flux is more complicated.

It is also pointed out that wave action might not exist in the unstable case, but the abovementioned conclusions are all still valid.