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The scattering of surface waves by structures intersecting liquid surfaces is fundamental in fluid mechanics, with prior studies exploring gravity, capillary and capillary–gravity wave interactions. This paper develops a semi-analytical framework for capillary–gravity wave scattering by a fixed, horizontally placed, semi-immersed cylindrical barrier. Assuming linearised potential flow, the problem is formulated with differential equations, conformal mapping and Fourier transforms, resulting in a compound integral equation framework solved numerically via the Nyström method. An effective-slip dynamic contact line model accounting for viscous dissipation links contact line velocity to deviations from equilibrium contact angles, with fixed and free contact lines of no dissipation as limiting cases. The framework computes transmission and reflection coefficients as functions of the Bond number, slip coefficient and barrier radius, validating energy conservation and confirming a$$90^\circ$$phase difference between transmission and reflection in specific limits. A closed-form solution for scattering by an infinitesimal barrier, derived using Fourier transforms, reveals spatial symmetry in the diffracted field, reduced transmission transitioning from gravity to capillary waves and peak contact line dissipation when the slip coefficient matches the capillary wave phase speed. This dissipation, linked to impedance matching at the contact lines, persists across a range of barrier sizes. These results advance theoretical insights into surface-tension-dominated fluid mechanics, offering a robust theoretical framework for analysing wave scattering and comparison with future experimental and numerical studies.
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Laboratory Measurements of Capillary-gravity Wave Scattering from Barriers with Contact Line Effects
Contact lines at a three-phase boundary (solid, liquid and air) play an essential role in the dynamics of the free surface of liquids in surface-tension-dominated fluids. While previous studies on the contact line effect have mainly focused on frequency and damping of standing wave modes in capillary dynamics, our study focuses on the contact line effect on capillary-gravity wave scattering from barriers. Models have predicted the contact line effects on capillary-gravity wave scattering from a barrier in ideal fluid configurations, but the lack of experimental data has hindered the progress. This research presents an experimental study that utilizes an acoustic approach to measure variations of the scattering with the barrier depth, barrier width, and surface wave frequency. Our study provides both evidence and quantitative measurements of the contact line effect on capillary-gravity wave scattering in realistic fluid configurations.
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- Award ID(s):
- 2306106
- PAR ID:
- 10609236
- Publisher / Repository:
- 76th Annual Meeting of the Division of Fluid Dynamics
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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