Rapid Perturbation Growth on Spatially and Temporally Varying Oceanic Flows Determined Using an Adjoint Method: Application to the Gulf Stream

Abstract

The stability of the Gulf Stream flow predicted by a nonlinear quasigeostrophic model is examined by employing an iterative method, which uses both the tangent linear equations and the adjoint tangent linear equations of the quasigeostrophic 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 mere localized and to grow much more rapidly than the normal modes. Optimal perturbations are of interest because they can be used to plan 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.