Influence of gravity on the frozen wave instability in immiscible liquids

Abstract

Gravity is crucial to the frozen wave instability because it both sets the threshold of applied forcing and limits the growth of unstable perturbations. Through numerical simulations of immiscible liquids in finite containers we examine the transition from a supercritical pitchfork bifurcation in ordinary gravity, which is accompanied by stable finite-amplitude waves, to a degenerate bifurcation in weightlessness, which is followed by large columnar patterns. The vibroequilibria effect plays a symmetry-breaking role in the bifurcation, selecting frozen waves with the heavier fluid displaced upward along the lateral walls.