Spatial evolution of a film flowing down a fiber

We report the response to a forcing at the inlet of a film flowing down a vertical fiber. Parameters are chosen in order to examine the effects of both inertia and surface tension. The spatial response of the film to inlet forcing depends on the ratio of the forcing frequency f_for to the frequency f_M corresponding to the maximum linear growth rate. At f_for≈f_M, the primary instability leads directly to the formation of a saturated wavetrain at the forcing frequency, whereas at low forcing frequencies f_for<f_M, this formation is preceded by a sequence of periodic coalescence events. The amplitude, speed, profiles, and inner flow pattern of traveling waves have been characterized and compared to the solutions to the two-equation model obtained by Ruyer-Quil [J. Fluid Mech. 603, 431 (2008)], showing a remarkable agreement. A steepening of the waves is observed when inertia becomes dominant. An excellent correlation between data is observed when the amplitude and speed of the waves are made dimensionless with reference to the substrate thickness and free-surface velocity.