Analytical Considerations of Lagrangian Cross-Equatorial Flow

Abstract

The Lagrangian description of cross-equatorial flow under any steady, strictly meridional, pressure gradient forcing is shown to comprise an integrable two-degree-of-freedom Hamiltonian system. The system undergoes a pitchfork bifurcation when the angular momentum passes through a critical value. It is shown that, even when the full variation of the Coriolis parameter is taken into account, the dynamical system is fully integrable, which implies that its evolution from any initial state can be calculated with sufficient accuracy (depending on the accuracy of the initial state) to any desired time. The role of the driving pressure gradient is merely to shift the latitude of the fixed points from their location in the inertial case. When zonal variation or time dependence of the pressure field is allowed, the system becomes nonintegrable and chaotic bands appear where nearby trajectories diverge exponentially.