Hyperchaos from a Model of Coupled Stratosphere-Troposphere Dynamics

Abstract

We present a six-dimensional system describing coupled troposphere-stratosphere dynamics which takes the form of two coupled Lorenz-84 systems (one for each of the troposphere and stratosphere) involving thermal forcing terms. The systems are coupled through a linear interaction term, which permits energy transfer between both troposphere and stratosphere layers. While other six-dimensional systems giving hyperchaos and multiscroll attractors have been found in the literature, the coupled systems given here arise naturally from the physical problem. In particular, the resulting six-dimensional system constitutes a physically interesting model where the stratosphere-troposphere dynamics are coupled to one another (rather than just coupling the troposphere dynamics to the stratosphere, while keeping the time evolution of the stratosphere independent). This model gives bounded dynamics and for some parameters exhibits chaos or hyperchaos. Interestingly, there are parameter regimes for which the dynamics go directly between periodic orbits and hyperchaos, bypassing an intermediate chaos step. The precise form of the coupling between the two Lorenz-84 systems is found to strongly influence the solution behavior. We find that even small coupling from the stratosphere back to the troposphere can destabilize the system and yield hyperchaotic dynamics, while for other parameter sets this coupling can instead yield smooth dynamics in both regions.