New graphical techniques for studying acoustic ray stability

Alternatives to the standard Poincaré section are proposed to cater for some conditions arising in the study of chaotic ray propagation where the usual method of dimension reduction by the Poincaré section is inadequate because the driving is not periodic. There are three alternatives proposed which all use the same surface of intersection, but which differ in their use of the values of the dependent variables at the intersections of the rays with the surface. The new reduction techniques are used to examine ray behaviour in a harmonically perturbed Munk profile which supports ray chaos. It is found that all three techniques provide a graphical means of distinguishing between regular and irregular motions, and that the space of the mapping associated with one of them is partitioned into nonintersecting regular and chaotic regions as with the Poincaré section. A further model with quasiperiodic time dependence of the Hamiltonian is examined, and it turns out that the quasiperiodic nature of the motion is revealed as Lissajous curves by one technique.