Optimal Perturbations with Zero Potential Vorticity in the Eady Model

Abstract

The problem of finding optimal perturbations, which are perturbations with a maximum ratio of the final energy to the initial energy, is considered in the Eady model of baroclinic instability. The solution to the problem uses explicit expressions for the energy functional, which are functions of parameters of an initial perturbation. For perturbations with zero potential vorticity, the basic parameters are the amplitudes of the initial buoyancy distributions at the boundaries of the atmospheric layer and a phase shift between these distributions. Dependences of the optimal phase shift and maximum energy ratio on the wave number and time optimization are determined using an analysis for extremum. The parameters of the optimal perturbations are compared with those of the growing normal modes. It is found that only one exponentially growing mode is an optimal perturbation.