The downstream evolution of disturbances, introduced at the inlet of a liquid film flowing along an inclined plane wall, is studied numerically by solving the full, time-dependent Navier–Stokes equation. Computational results are validated against the predictions of spatial linear stability analysis and against detailed data of the entire evolution process. The structure of the flow field below the waves is analyzed, and the results are used to test assumptions frequently invoked in the theoretical study of film flow by long-wave equations. An interesting prediction is that solitary waves exhibit strongly nonparabolic velocity profiles in front of the main hump, including a slim region of backflow. The computational scheme is subsequently used to study solitary wave interactions. It is predicted that coalescence (the inelastic collision of two humps) is not inevitable but occurs only when the waves differ appreciably in height. Waves of similar size repel monotonically, whereas for intermediate differences in height a strong oscillatory interaction between the two humps is predicted. Encouraging qualitative agreement with the limited experimental information available is noted.
Experimental results are reported on the structure of gravity-driven film flow along an inclined periodic wall with rectangular corrugations. A fluorescence imaging method is used to capture the evolution of film height in space and time with accuracy of a few microns. The steady flow is found to exhibit a statically deformed free surface, as predicted by previous asymptotic and numerical studies. Though usually unstable, its characteristics determine much of the subsequent non-stationary dynamics. Travelling disturbances are observed to evolve into solitary multi-peaked humps, and pronounced differences from the respective phenomena along a flat wall are noted. Finally, a remarkable stabilization of the flow at high Reynolds numbers is documented, which proceeds through the development of a three-dimensional flow structure and leads to a temporary decrease in film thickness and recession of solitary waves.
Experimental results are reported on non-stationary evolution and interactions of waves forming on water and water–glycerol solution flowing along an inclined plane. A nonlinear wave generation process leads to a large number of solitary humps with a wide variety of sizes. A uorescence imaging method is applied to capture the evolution of film height in space and time with accuracy of a few microns. Coalescence – the inelastic interaction of solitary waves resulting in a single hump – is found to proceed at a timescale correlated to the difference in height between the interacting waves. The correlation indicates that waves of similar height do not merge. Transient phenomena accompanying coalescence are reported. The front-running ripples recede during coalescence, only to reappear when the new hump recovers its teardrop shape. The tail of the resulting solitary wave develops an elevated substrate relative to the front, which decays exponentially in time; both observations about the tail confirm theoretical predictions. In experiments with water, the elevated back substrate is unstable, yielding to a tail oscillation with wavelength similar to that of the front-running ripples. This instability plays a key role in two complex interaction phenomena observed: the nucleation of a new crest between two interacting solitary humps and the splitting of a large hump (that has grown through multiple coalescence events) into solitary waves of similar size.
Gravity-driven film flow along an inclined periodic wall with transverse rectangular corrugations is studied experimentally. The effect of corrugation steepness (=height∕length) is considered in detail and an interesting contrast emerges between properties of the flow that are apparently independent of corrugation steepness and properties that are strongly affected by it. The steady interaction between the wall and the flow leads to a statically deformed free surface, whose amplitude is independent of the corrugation heights tested. Beyond the maximum steady free-surface amplitude, a three-dimensional pattern is established (consisting of transverse arrays of depressions along corrugation valleys), again at conditions independent of corrugation height. On the contrary, steep corrugations expand significantly the stable region of steady flow. Also, fully developed traveling waves (emerging from ambient noise under unsteady conditions) are significantly larger and more regular than under the same conditions along a flat wall. This difference is attributed to the continuous interaction of traveling pulses with the steadily deformed substrate.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.