Optimal Excitation of Baroclinic Waves

Abstract

Development of perturbations in a baroclinic flow can arise both from exponential instability and from the transient growth of favorably configured disturbances that are not of normal mode form. The transient growth mechanism is able to account for development of neutral and damped waves as well as for an initial growth of perturbations asymptotically dominated by unstable modes at significantly greater than their asymptotic exponential rates. Unstable modes, which are the eigenfunctions of a structure equation, are discrete and typically few in number. In contrast, disturbances favorable for transient growth form a large subset of all perturbations. To assess the potential of transient growth to account for a particular phenomena it is useful to obtain from this subset the initial condition that gives the maximum development in a well-defined sense. These optimal perturbations have a role in the theory of transient development analogous to that of the normal modes in exponential instability theory; for instance they are the structures that the theory predicts should be found to precede rapid development. In this work optimal perturbations for the excitation of baroclinic stable and unstable waves are found. The optima are obtained for the formation of synoptic scale cyclones as well as for the development of planetary scale stationary and transient baroclinic Rossby waves. It is argued from these examples that optimal perturbations are likely to limit predictability on time scales relevant to the short and medium range forecast problem and that unstable modes, if present, dominate the long range forecast.