Symmetry Breaking in Large Columnar Frozen Wave Patterns in Weightlessness

Abstract

The large columnar patterns resulting from the frozen wave instability in zero gravity conditions are investigated numerically for finite containers of immiscible liquids. The mode selection process is affected by forcing amplitude, frequency, container size and the vibroequilibria effect. The final columnar states are often approximately left-right symmetric and a quantitative measure of their asymmetry is used to distinguish three different growth regimes depending on the applied vibration. Solutions at low frequencies are affected by the antiphase forcing at the lateral walls and by early collisions of the longwave modes with the upper and lower boundaries. At moderate frequencies, the development of the pattern is characterized by centrally located defects and nearly symmetric modes. At higher frequencies, there are off-center defects and asymmetric modes. The critical value of the symmetry-breaking transition separating these final two types of behavior is determined as a function of the container aspect ratio.