Two-parameter study of the quasiperiodic route to chaos in convecting ^{3}-^{4}He mixtures

Abstract

We study the frequency lockings of two intrinsic hydrodynamic modes of a convecting $^{3}\mathrm{\ensuremath{-}}^{4}$He mixture by independently varying the Rayleigh and Prandtl numbers. We establish points on the critical line in this parameter space using a transient technique to locate the spiral-node transition in the interior of three resonance horns. Universal scaling is demonstrated at winding numbers with golden mean tails by computing the f(\ensuremath{\alpha}) singularity spectrum.