Nonuniform broken-parity waves and the Eckhaus instability

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Abstract
We report measurements on broken-parity traveling finger patterns which form at an oil-air interface driven by the rotation of two acentrically mounted horizontal cylinders. In the parameter region studied here, the wavelength, traveling speed, and degree of asymmetry of the traveling fingers vary along the interface. As our control parameter is increased, we observe a transition at which the average values of these properties suddenly decrease. The traveling patterns are intermittently interrupted by periods of disordered behavior, which become more frequent near this transition. The variation of wavelength along the pattern allows us to observe what appears to be the Eckhaus instability: outside a range of wavelengths, the drifting fingers become unstable, resulting in the birth of new fingers if the local wavelength is too long, or the disappearance of a finger if it is too short. We measure the Eckhaus stability boundary for this system.