Interpretation of discrete and continuum modes in a two-layer Eady model

Abstract

The upper rigid lid of the conventional Eady model for baroclinic instability is replaced by a more realistic stratosphere with an increased buoyancy frequency and a different shear of the zonal wind. Previously reported results of a normal-mode stability analysis are re-interpreted using the concept of interacting surface and tropopause PV anomalies, called PV building blocks (PVBs). In this perspective, which directly relates to the counter-propagating Rossby wave formalism, the appearance of both the short-wave and the long-wave cut-off becomes physically transparent. New results include a discussion of the continuum modes in terms of interacting PVBs. Continuum modes are modal solutions to the inviscid linearised equations, specified by non-zero PV at one interior level (as well as non-zero PV at the surface and the tropopause). If the stratospheric zonal wind decreases with height, the continuum modes cause resonances at multiple (even stratospheric) levels. These resonant continuum modes may play an important role in the explanation of disturbance growth from initial conditions in which the discrete normal modes are neutral.