Subharmonic Bifurcation Cascade of Pattern Oscillations Caused by Winding Number Increasing Entrainment

Abstract

Convection structures in binary fluid mixtures are investigated for positive Soret coupling in the driving regime where solutal and thermal contributions to the buoyancy forces compete. Bifurcation properties of stable and unstable stationary square, roll, and crossroll structures and the oscillatory competition between rolls and squares are determined numerically as a function of fluid parameters. A novel type of subharmonic bifurcation cascade where the oscillation period grows in integer steps as $n\frac{2\ensuremath{\pi}}{\ensuremath{\omega}}$ is found and elucidated to be an entrainment process.