For a given flow, one may identify those disturbances which amplify most rapidly over a fixed time interval, for a given norm. These "optimal" disturbances (are the "singular vectors" (SV's) of the linear operator which describes the evolution of the fluid system.
In this presentation, the basic mechanisms for development of SV's in a hierarchy of rather simple QG models (Eady, Green, and Charney models) are discussed. The salient features of the transient development of these singular vectors are then identified and characterized by the SV's evolving PV distribution. Rather than appealing to the underlying mathematics describing the SV evolution, piecewise PV diagnostics are applied to interpret the SV evolution in terms of the evolution of the SV's interior PV and boundary potential temperature distributions. Decomposition of the SV's into modal structures (normal modes and continuous spectrum (CS) structures) reveals the role these modes play in the development. It will be shown that the modal decomposition of the SV's reveals that the continuous spectrum plays a detrimental (positive) role in the development for sufficiently long (short) waves. The structure of the CS is described and interpreted in terms of its PV and BT characteristics.
In subsequent presentations, detailed diagnostic studies of SV evolution in the Eady model for varying optimization times and norms will be presented.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics