Petterssen's “Type B”Cyclogenesis in Terms of Discrete, Neutral Eady Modes

Abstract

We investigate B. Farrell's hypothesis that the development of a surface cyclone with the passage of an upper trough, as observed by S. Pettessen and coworkers, may be understood in terms of an initial-value problem on the Eady model. We consider the response of the Eady model to perturbations whose horizontal wavelengths are short enough to ensure their stability, and whose perturbation potential vorticity is zero. We depart from Farrell with the latter condition as it eliminates the continuous spectrum and allows the evolution of the perturbation to be understood solely in terms of the two normal modes of the Eady model?one with maximum amplitude at the upper lid, which propagates eastward with respect to the midlevel flow, and one westward propagating, with maximum amplitude at the lower surface. Imagine an initial upper-level disturbance with no surface perturbation; this is represented by the two Eady modes in combination such that the initial surface perturbation pressure is zero. As the flow evolves out of this initial condition, a pressure disturbance appears at the surface as the two modes propagate past one another. That is, a surface cyclone forms, deepens, and then weakens, as the upper trough passes. This amplification of the surface trough is not due to mere geometrical interference, but rather is the consequence of an energy-exchanging interplay between waves and mean flow. This distinction is emphasized by comparison with a model in which a superficially similar phenomenon occurs, but without such an interplay.