Data Assimilation, P. P. Brasseur and J. C. J. Nihoul Eds., Springer-Verlag, Berlin The goal of the project on stability of ocean flows is to develop the theory of linear stability appropriate for understanding the growth of perturbations in dynamical systems with emphasis on oceanic applications. The theory is based on analysis of the non-normality of the dynamical operator and it subsumes the traditional modal stability theory and extends it naturally to time scales for which time asymptotic modal theory is inappropriate as well as to time dependent systems where the modal ansatz can not be made.

The stability of the Gulf Stream flow is predicted by a nonlinear quasigeopstophic model is examined by employing an interactive method, which uses both the tangent linear equations and the adjoint tangent linear equations of the quasigestrophic model. The basic state flow is the model's representation of the Gulf Stream as observed during January and February 1988. The growth of perturbation energy is examined as a measure of disturbance growth and linear perturbations are found that are optimal in the sense that they maximize the growth of perturbation energy. The structures of optimal perturbations are compared with the structure of the normal modes. The optimal perturbations are found to be more localized and grow much more rapidly than the normal modes.

Optimal perturbations are of the interest because they can be used to place tight constructive upper bounds on the growth of perturbations to ocean currents such as the Gulf Stream, and they provide valuable information about the predictability of such flows.

Initially the stability of a basic-state flow that is stationary in time is considered. The inclusion of time dependence in the basic state is straightforward using the method adopted here, and it is found that the time evolution of the basic-state flow can have a large influence on the structure and preferred location of the optimal perturbation.

This work explores the formation and growth of waves on oceanic flows using a quasigeostrophic model. In participial, we consider flow regimes consisting of zonal oceanic jets, similar in face to the westward extension of the Gulf stream. Traditionally, the formation of waves had been ascribed to exponentially unstable modes, but rather than adopt this paradigm, we seek the most rapidly growing perturbation without restriction of its structure to normal-mode form. Optimal excitations are determined using the adjoint of the quasigeostrophic dynamic equations, and the perturbations found by this method are shown to grow more rapidly than the unstable mode.

Applications of the theory presented here include determination of a tight upper bound on perturbation growth rate, a constructive method for finding the most disruptive disturbance to a given flow, and a methods for determining the relative predictability of flows from the form of the most rapidly growing perturbation, resolution requirements for the numerical models can be determined.