A Non-normal View of the Wind-Driven Ocean Circulation

Abstract

Generalized linear stability theory is applied to the wind-driven ocean circulation in the form of a double gyre described by the barotropic quasigeostrophic vorticity equation. The development of perturbations on this circulation is considered. The circulation fields are inhomogeneous, and regions of straining flow render non-normal the tangent linear operators that describe the time evolution of perturbation energy and enstrophy. When the double-gyre circulation is asymptotically stable, growth of perturbation energy and enstrophy is still possible due to linear interference of its nonorthogonal eigenmodes. The sources and sinks of perturbation energy and enstrophy associated with the interference process are traditionally associated with the interaction of perturbation stresses with the mean flow. These ideas are used to understand the response of an asymptotically stable double-gyre circulation to stochastic wind stress forcing. Calculation of the optimal forcing patterns (stochastic optimals) reveals that much of the stochastically induced variability can be explained by one pattern. Variability induced by this pattern is maintained by long and short Rossby waves that interact with the western boundary currents, and perturbation growth occurs through barotropic processes. The perturbations that maintain the stochastically induced variance in this way have a large projection on some of the most non-normal, least-damped eigenmodes of the double-gyre circulation. Perturbation growth in nonautonomous and asymptotically unstable systems is also considered in the same framework. The Lyapunov vectors of unstable flows are found to have a large projection on some of the most non-normal, least-damped eigenmodes of the time mean circulation.