The dynamics of a low-order coupled ocean-atmosphere model

Abstract

A system of ve ordinary dierential equations is studied which combines the Lorenz model for the atmosphere and a box model for the ocean The behaviour of this system is studied as a function of the coupling parameters For most parameter values the dynamics of the atmosphere model is dominant Stable equilibria are found as well as periodic solutions and chaotic attractors For a range of parameter values competing attractors exist The KaplanYorke dimension and the correlation dimension of the chaotic attractor are numerically calculated and compared to the values found in the uncoupled Lorenz model The correlation dimension diers much less than te KaplanYorke dimension indicating that there is little variability in the ocean model In the transition from periodic behaviour to chaos intermittency is observed This is explained by means of bifurcation analysis The intermittent behaviour occurs near a NeimarkSacker bifurcation at which a periodic solution loses its stability The average length of a periodic interval in the intermittent regime l is studied as a function of the bifurcation parameter Near the bifurcation point it shows a power law scaling It diverges as l where and is the distance from the bifurcation point in reasonable agreement with the results of Pomeau and Manneville Commun Math Phys The intermittent behaviour persists beyond the point where the unstable periodic solution disappears in a saddle node bifurcation The length of the periodic intervals is governed by the time scale of the ocean component Thus in this regime the ocean model has a considerable inuence on the dynamics of the coupled system