Non-parallel flow effects on the stability of film flow down a right circular cone

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Abstract
A global asymptotic solution for the linear stability of this flow with respect to axisymmetric disturbances is developed without invoking the usual quasi-parallel flow assumption. This solution predicts the occurrence of quasi-periodic spatially amplified disturbances relatively near the apex, which ultimately are stabilized further down the cone by the relative increase in viscous forces associated with the progressive thinning of the film. The wave speed and wavelength of these disturbances are found to decrease with increasing distance from the apex.