Chaotic trajectories of tidally perturbed inertial oscillations

Abstract

It is shown that tidal perturbations of a geopotential height in an inviscid, barotropic atmosphere can turn a purely inertial, predictable trajectory of a Lagrangian particle chaotic. Hamiltonian formulation of both the free, inertial, and the tidally forced problems permitted the application of the twist and KAM theorems, which predicts the existence of chaotic trajectories in the latter case. The chaotic behavior manifests itself in extreme sensitivity of both the trajectory and the energy spectra to initial conditions and to the precise value of the perturbation's amplitude. In some cases dispersion of initially close particles can be very fast, with an e-folding time of the rms particle separation as high as one day. A vigorous mixing is induced by the chaotic advection associated with the tidal forcing through the stretching and folding of material surfaces. -Authors