Stratified flows in hydrostatic balance are studied in both their multilayer and continuous formulations. A novel stability criterion is proposed for stratified flows, which reinterprets stability in terms not of growth of small perturbations but of the well-posedness of the time evolution. This reinterpretation allows one to extend the classic results of Miles and Howard concerning steady and planar flows to the realm of flows that are nonuniform and unsteady.
Chumakova, L., Menzaque, F. E., Milewski, P. A., Rosales, R. R., Tabak, E. G., & Turner, C. V. (2009). Shear instability for stratified hydrostatic flows. Communications on Pure and Applied Mathematics, 62(2), 183-197. https://doi.org/10.1002/cpa.20245