A study of barotropic decay with finite amplitude wave theory

Small-amplitude wave activity quantities such as pseudomomentum and pseudoenergy have been used to analyze wave-mean flow interactions. We extend the notions of pseudomomentum and pseudoenergy as finite amplitude diagnostics for breaking Rossby wave, mean flow modification and mixing. With the finite amplitude pseudomomentum density, A*, introduced by Nakamura and collaborators (2010), we revisit the example of a barotropic decay of a wave-like disturbance in a shear flow examined by Held & Phillips (1987). We demonstrate (1) how the evolution of A* can be partitioned precisely between the mean flow modification, Eliassen-Palm (E-P) flux and dissipation due to mixing and (2) the sensitivity of a new reference state uREF to irreversible mixing. This new finite amplitude wave theory provides a theoretical framework for atmospheric phenomena involving wave breaking, such as tropospheric blocking and stratospheric sudden warming.