Non-normal growth in symmetric shear flow

An analysis of symmetric instability from the perspective of Generalized Stability Theory is presented. For Richardson number smaller than one, the optimal growth exceeds that predicted by normal mode analysis yielding potentially a much faster generation of slantwise convection. In both normal and non-normal evolution, the parcel trajectory remains close to the isentropes and energy growth results primarily from the vertical Reynolds stress term in the energy equation. The large non-normal growth obtained results from the optimal perturbations having parcel trajectories in the mean shear plane, in the initial stage, that maximize the growth by Reynolds stress. This plane is perpendicular to the plane of the isentropes and the absolute momentum isolines, usually associated with slantwise convection. For Richardson number larger than unity, transient growth results primarily from the meridional heat flux term in the energy equation, however this growth is relatively small.