Bifurcation in Cross-Equatorial Airflow: A Nonlinear Characteristic of Lagrangian Modeling

Abstract

Low-level monsoonal cross-equatorial airflow is investigated using a simple Lagrangian model for the tropical atmosphere. With the use of Jacobian elliptic functions, analytical solutions for the dynamic system are obtained to an extent that enables the most interesting features of the model to be demonstrated. It is found that there exists some unpredictability with the equatorial airflow, in the sense that the trajectory of the airflow can either remain in one hemisphere or cross the equator from one hemisphere to another depending upon the value of a model parameter ?c being negative or positive, even when the corresponding external forcings are of little difference. By means of qualitative analysis of the dynamic system, some more esoteric properties of the model solutions are investigated. It is found that the model exhibits a very interesting bifurcation, which explains the unpredictability. The bifurcation is a characteristic attributable to the nonlinearity of the Coriolis term in the Lagrangian model. Since the Coriolis term is linear in a dynamically identical Eulerian model, the characteristic would not be explicitly revealed by Eulerian modeling. By numerical method, the model is extended and applied to the simulation of cross-equatorial airflow in the context of Australian monsoon. The exercise provides an example of how to bridge the gap between a simplified analytical model and the realities of the actual tropical meteorology.