Resonant and quasi-resonant excitation of baroclinic waves in the Eady model

The structure of baroclinic waves in a geostrophic flow with a constant vertical shear (Eady model) is very consistent with that of atmospheric vortex formations. This paper proposes an approach to describing the generation of these waves by initial perturbations of potential vorticity (PV). Within the framework of the suggested approach, the solution to the initial-value problem for a quasi-geostrophic form of the PV transfer equation is represented as a sum of the wave and vortex components with zero and nonzero PV, respectively. A set of ordinary differential equations with the right-hand side dependent on the vertical PV distribution is formulated using Green functions for the amplitude of the wave component (amplitude of excited baroclinic waves). The solution provides a simple description of the resonant and quasi-resonant baroclinic-wave excitation effects under which the wave amplitude grows according to the linear or logarithmic laws. These types of excitation take place for singular and discontinuous initial PV distributions if the frequencies of the wave and vortex components coincide. Smooth distributions generate finite-amplitude waves.