EADY EDGE WAVES AND RAPID DEVELOPMENT

Perturbations of the classical Eady model are treated in terms of the system's two intrinsic baroclinic edge waves. This provides a simple q uantitative example of the wave coupling interpretation of quasigeostr ophic instability and a compact framework for examining the rudiments of upper level-lower level dynamical interaction. The reformulation co nsolidates and extends a series of earlier theoretical results: the ex istence of transient growth at wavenumbers beyond the Eady cutoff scal e, the disparity between different measures of the maximum instantaneo us growth rate with the highest values being associated with thermal ( pressure) development at large (small) wavelengths, the existence of m aximum instantaneous thermal growth rates substantially exceeding that of the Eady normal modes, and the vertical alignment of the couplet m ost favorable for initial rapid development-quadrature phase of the th ermal (pressure) components for optimum thermal (pressure) growth. The re is also diversity in the finite time evolution of couplets. Short w avelength couplets undergo a periodic temporal development with compar atively mild amplitude changes. Longer-scale couplets asymptote toward the counterpart Eady normal mode. The latter achieve maximum thermal growth in a stipulated time if the relative phase of the couplet trans its symmetrically through the quadrature configuration, and the fastes t growing couplet can typically sustain a thermal amplitude doubling i n approximately 6 hours and a fivefold increase in approximately 24 ho urs, During such development the eastward thermal slope of the very lo ng (intermediate) scale couplets become less (more) inclined to the ve rtical. It is further shown that a coherent packet of edge wave couple ts can evolve rapidly (approximately 1 day) from a suitably shaped ini tial disturbance composed predominantly of either ultralong or interme diate-scale waves. The vertical structure of the emerging intermediate -scale packet is akin to that of observed atmospheric developments. Th e edge wave formulation is also used to explore the effect of interior PV perturbations. Consideration of the influence of an idealized, but elemental, potential vorticity distribution upon a surface edge wave leads to inferences regarding the cyclogenetic potential of certain at mospheric flow structures.