Unstable periodic orbits and attractor of the barotropic ocean model

Abstract. A numerical method for detection of unstable periodic orbits on attractors of nonlinear models is proposed.  The method requires similar techniques to data assimilation.  This fact facilitates its implementation for geophysical models.  This method was used to find numerically several low-period orbits for the barotropic ocean model in a square.  Some numerical particularities of application of this method are discussed. Knowledge of periodic orbits of the model helps to explain some of these features like bimodality of probability density functions (PDF) of principal parameters.  These PDFs have been reconstructed as weighted averages of periodic orbits with weights proportional to the period of the orbit and inversely proportional to the sum of positive Lyapunov exponents. The fraction of time spent in the vicinity of each periodic orbit has been compared with its instability characteristics. The relationship between these values shows the 93% correlation.  The attractor dimension of the model has also been approximated as a weighted average of local attractor dimensions in vicinities of periodic orbits.