Diagnosis of Optimal Perturbation Evolution in the Eady Model

Abstract

Abstract The structure and evolution of Eady model singular vector (SV, also referred to as optimal perturbation) streamfunction perturbations are described using a combination of two different partitions of the vector subspace describing all possible streamfunction perturbations. A modal partitioning of the SV perturbation streamfunction (expressing the SV streamfunction as a linear combination of modal structures) is used to ascribe the roles and relative importance of the continuum modes (CMs) and the discrete normal modes (NMs) in SV initial structure and subsequent evolution. In addition, a potential vorticity (PV) partitioning of the SV perturbation streamfunction into parts attributed to the SV PV and the SV boundary thermal anomalies (BTAs) is employed. The structures of the CMs and NMs are described in terms of their characteristic perturbation PV and BTAs. Modal decomposition of the SVs reveals that for all zonal wavenumbers (k), the NMs have the largest projection coefficients (with magnitudes ...