Scale-dependent properties of optimal perturbations on a zonally varying barotropic flow

The scale-dependent characteristics of the optimal perturbations in a zonally asymmetric barotropic model are examined. The dependence of the optimal energy growth on the initial scale is investigated through the calculations of spectrally constrained optimal perturbations. Considering an optimization time of τ = 3 days, and a basic state containing an idealized Asian jet, the optimal amplification factor generally increases with the decrease of the imposed initial scale. In the absence of diffusion, the most amplifying scale becomes the smallest scale in the model. An energetics analysis shows that the energy conversion in the optimal excitation process is dominated by the shear straining term, with a sharp increase in the scale of the perturbation accompanying the explosive energy growth. These results show the similarity between the optimally growing process in the zonally asymmetric system and the shear straining process in a parallel shear flow. Except when a small τ is considered or a sufficiently strong diffusion is used in the system, the optimal energy growth for small-scale disturbances sensitively depends on the zonally varying feature of the basic state. With τ = 3 days, the optimal amplification factors for small-scale disturbances are reduced significantly when the idealized Asian jet is shortened by only one-fifth. At the same time, those for medium- and large-scale disturbances are almost unaffected by the change of the basic state. The reasons for this contrast of the sensitivity property between the small and large scales are discussed.