Chaos of a simple coupled system generated by interaction and external forcing

Abstract

¶This paper is concerned with the chaotic behavior of a coupled system consisting of two components, one representing the atmosphere and the other representing the ocean. The system is expressed as a highly truncated spectral model and for each component, the spectral model is similar to that of Lorenz (1963). Interactions between the two components are permitted, which lead to the temporal variation of surface temperature and hence that of a critical model parameter (the Rayleigh number). The emphasis of the paper is placed upon the chaotic behavior arising from the interactions between the two components and from periodic external forcing. Numerical tests are carried out to show that through interactions, the chaotic behavior of one component may result in chaos of the other even if the latter is otherwise stationary or periodic. It is shown that chaos may also occur if the system is forced periodically at certain frequencies. This study indicates that a new mechanism for chaos exists for coupled systems which are subject not only to internal fluid dynamic nonlinear interactions, but also to interactions between different components and external forcing.