Optimal Growth of Antarctic Circumpolar Waves

Abstract

Abstract Generalized stability theory is applied to a simple dynamical model of interannual ocean–atmosphere variability in the southern midlatitudes to determine the perturbations that create the most rapid growth of energy in the system. The model is composed of a barotropic quasigeostrophic atmosphere coupled to a 1.5-layer quasigeostrophic ocean, each linearized about a zonally invariant mean state, and with atmospheric and ocean surface temperature obeying a simple heat balance. Eigenanalysis of the system reveals modes of interannual variability that resemble the so-called Antarctic Circumpolar Wave (ACW), consistent with an earlier analytical study of the system. The optimal excitation of these modes relative to an energy norm is found to be a perturbation almost entirely restricted to the ocean momentum field and is shown to resemble strongly the optimal perturbations in energy for the system. Over interannual time scales most rapid growth is seen in zonal wavenumbers 4–6, despite the fact that the least-damped eigenmodes of the system are of a lower zonal wavenumber. The rapid transient growth in energy occurs by extracting perturbation energy from the mean state through advection of the mean meridional oceanic temperature gradient. This transient growth of high-zonal-wavenumber modes dominates the model’s variability when it is forced by noise that is white in space or time. A dominant low-zonal-wavenumber response, consistent with the observed and modeled ACW, occurs only when the forcing is red in space or time, with decorrelation scales greater than 3 yr or 10 000 km. It is concluded that, if the ACW is a coupled mode analogous to that supported in this simple model, then it is excited by other large-scale phenomena such as ENSO rather than by sources of higher-frequency forcing.