Resonant Continuum Modes in the Eady Model with Rigid Lid

Abstract

Abstract The Eady model with rigid upper lid is considered. The resonant, linearly amplifying solution that exists in the situation of neutral normal modes when an infinitely thin potential vorticity (PV) perturbation is located precisely at the steering level of a zero-PV neutral mode is explicitly derived. This resonant solution is discussed by partitioning the solution into nonzero-PV and zero-PV contributions. It possesses key observed properties of a growing baroclinic structure. The partitioning of the resonant solution clearly demonstrates the existence of modal growth in a short-wave Eady setting. In contrast to the semi-infinite model, a nonamplifying zero-PV contribution is necessary, in addition to the resonant part, to ensure vanishing vertical velocity at both the upper and the lower lid.