Scaling at the Transition from Quasiperiodicity to Chaos in a Hydrodynamic System

Abstract

Universal scaling properties have been predicted for the transition from quasiperiodicity to chaos. We have tested the applicability of these predictions, which are based on the behavior of circle maps, to a hydrodynamic system (Rayleigh-Bénard convection) in which a limit cycle was perturbed at a second frequency to generate a flow on a torus in phase space. The ratio of the two frequencies was adjusted to within about 0.1% of the inverse of the golden mean. Some evidence for spectral self-similarity was found. Phase locking at a nearby rational ratio changes the spectrum qualitatively.