Instability of 2D flows to hydrostatic 3D perturbations

Straub discusses the evolution of three-dimensional perturbations to the hydrostatic equations linearized about a two-dimensional base state. The study begins with the non-rotating, unstratified case, and draws analogies between the perturbation equations and equations describing evolution of material line elements and scalar gradients embedded in the same two-dimensional flow. Also considered is the effect of a constant stratification, where perturbation equations can then be separated into vertical modes that have simple sinusoidal structures.