Conditional nonlinear optimal perturbations of the double-gyre ocean circulation

In this paper, we study the development of finite amplitude perturbations on linearly stable steady barotropic double-gyre flows in a rectangular basin using the concept of Conditional Nonlinear Optimal Perturbation (CNOP). The CNOPs depend on a time scale of evolution te and an initial perturbation threshold δ. Under symmetric wind forcing, a perfect pitchfork perturbation occurs in the model. The CNOPs are determined for all linearly stable states and the time evolution of the CNOPs is studied. It is found that the patterns of the CNOPs are similar to those of the non-normal modes for small te and approach those of the normal modes for larger te. With slightly asymmetric winds, an imperfect pitchfork occurs in the model. Indications are found that the time evolution of the CNOPs is related to the value of the dissipation function of the underlying steady state.