Homoclinic Dynamics: A Scenario for Atmospheric Ultralow-Frequency Variability

Abstract

In this paper, a link will be established between atmospheric ultralow-frequency variability (ULFV) and the occurrence of homoclinic dynamics in models of large-scale atmospheric flow. It is known that uncoupled atmosphere models possess significant variability on very long timescales (years to decades), which must be generated by internal atmospheric dynamics. The mathematical structure of this long-timescale variability is investigated, using a global two-layer atmosphere model formulated in terms of preferred flow patterns (EOFs). Due to its efficient formulation, this model can simulate an atmospheric flow with realistic features, using only a small number of degrees of freedom. The 10-dimensional version of the model possesses both nonzero ultralow-frequency variability and several realistic short timescales. The essence of the ultralong timescale behavior of the 10D model, which manifests itself as bursting in the atmospheric turbulent energy, can be represented by a four-dimensional subsystem. In this subsystem, strong evidence for the existence of a homoclinic orbit is found. The chaotic dynamics generated by the homoclinic orbit explains the occurrence of ultralong timescales in the model. It is argued that hints of homoclinic dynamics can also be found in more complex models. As an example, a T21 barotropic atmosphere model (231 dimensions) of the Northern Hemisphere is shown to possess behavior that suggests the existence of a homoclinic orbit.