Explaining the growth of disturbances superimposed on mean flows is a central problem in meteorology. Most widely studied models of the development process involve perturbations to shear flows with shear restricted to the meridional direction. Recently the importance of zonal variation of the mean flow was recognized and the study of shear flows extended to include zonal variation in shear. These studies found that the eigenfunctions associated with unstable modes in the simple shear problem are highly sensitive to zonal variation of the mean flow. However, there also exists another mechanism for development in a zonally inhomogeneous flow field: transient growth not associated with exponential instability. Properly configured perturbations exhibit transient growth in deformation fields associated with regions of confluence and diffluence at rates comparable to development in shear flow.
In this work analytic solution of the linear initial value problem for the barotropic vorticity equation in deformation flow is used to construct local perturbations that undergo rapid transient development. Implications for cyclogenesis and block formation are discussed.