Vibration-induced instability of a fluid film flowing down a vertically inclined plane: Experimental and theoretical comparison

This paper validates the theory of linear stability as applied to a fluid flowing down a vertically inclined plane using experimental comparison. The theoretically predicted mode 1 instability, corresponding to a surface wave oscillating at half the forcing frequency, is found to exist alongside the mode 2 instability, corresponding to a surface wave oscillating at the forcing frequency. Instability onset amplitude and frequency were compared, and an investigation of wavenumber with forcing amplitude at several distinct frequencies further confirmed the validity of the theory. A study of the wavenumber trend revealed distinct differences in the stability and development of the surface wave with increasing forcing amplitude. An analysis of the Womersley number, which expresses the ratio of the oscillatory inertia force to the viscous shear force, provides a physical indication of the differences in the wavenumber trend observed. Published by AIP Publishing.