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A Framework for the Automation of Generalized Stability Theory

The traditional approach to investigating the stability of a physical system is to linearize the equations about a steady base solution, and to examine the eigenvalues of the linearized operator. Over the past several decades, it has been recognized that this approach only determines the asymptotic stability of the system, and neglects the possibility of transient perturbation growth arising due to the nonnormality of the system. This observation motivated the development of a more powerful generalized stability theory (GST), which focuses instead on the singular value decomposition (SVD) of the linearized propagator of the system. While GST has had significant successes in understanding the stability of phenomena in geophysical fluid dynamics, its more widespread applicability has been hampered by the fact that computing the SVD requires both the tangent linear operator and its adjoint: deriving the tangent linear and adjoint models is usually a considerable challenge, and manually embedding them inside ...