On the Parcel Method and the Baroclinic Wedge of Instability

Abstract

The heuristic explanation, suggested by the parcel method, for the baroclinic instability mechanism is reexamined. The parcel method argues that an air parcel displaced within the wedge of instability, that is, between the horizontal and the isentropes, is vertically accelerated by the buoyancy force and hence becomes unstable. However, in the synoptic scale, the buoyancy is balanced by the vertical pressure gradient force perturbation, which is neglected by the parcel method, and thus the parcel acceleration is essentially horizontal. For the unstable Eady normal modes, the horizontally averaged buoyancy work is found to maximize at the steering level and to vanish at the boundaries, but the horizontally averaged parcel kinetic energy growth is minimized at the steering level and maximized at the boundaries. It is shown that the buoyancy work is vertically redistributed by the pressure gradient force perturbation throughout the secondary circulation. The parcel method also assumes that a parcel displaced adiabatically within the wedge of instability finds itself warmer than its new surroundings and thus contributes toward both vertical and meridional positive heat fluxes. However, since the temperature difference between the parcel and the environment from which it departed cannot be neglected, the slope of the instantaneous displacement is not a sufficient criterion to determine the signs of the heat fluxes. It is shown here that for the Eady normal modes solution, the four combinations of ascending or descending of initially colder or warmer parcels make jointly the vertical heat flux maximize at the steering level and the meridional heat flux remain constant with height.