Whirling hexagonal convection in a rotating binary-alloy mushy layer

Abstract

We study small amplitude convection in a mushy layer rotating about the vertical axis during binary-alloy solidification. The variation of permeability with the local solid fraction, an inherent property of the mushy layers, has been known to be responsible for three-dimensional steady hexagons as a preferred pattern near the onset of convection. We find that rotation manifests itself in a breaking of the chiral symmetry, giving rise to a secondary instability in the form of oscillating hexagons. We derive the amplitude equations governing the weakly-nonlinear evolution near this chiral-symmetry breaking. We localise the secondary bifurcation points identifying the regime of oscillating hexagons and analyse their parametric dependencies. We propose parameter conditions to approach the regime of oscillating hexagons in potential experiments.