Symmetry-breaking instabilities on a fluid surface

A sequence of symmetry-breaking instabilities leading to a chaotic state has been discovered in the surface deformations of a fluid layer subjected to a vertical oscillation. For driving amplitudes above a critical value, a primary instability leads to circularly symmetric standing waves at half the driving frequency. A second instability at a higher threshold breaks the circular symmetry and leads to a slow precession of the pattern, so that the overall motion is quasiperiodic. Beyond a third threshold, azimuthal modulations produce chaotic time dependence A fourth instability leads discontinuously to a spatially disordered flow. The spatial structure associated with each instability has been determined qualitatively, and the frequency spectrum of the local surface deformation has been measured using a sensitive laser deflection technique.