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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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This content will become publicly available on December 25, 2025
Numerical Investigations of Capillary-Gravity Wave Scattering by a Cylindrical Barrier
The scattering of surface waves by structures intersecting a liquid surface has long been a focus in fluid dynamics due to its theoretical and practical implications. Historically, theoretical studies on this problem have predominantly employed idealized assumptions such as infinitesimally thin barriers, which do not fully represent real-world conditions. This project aims to extend the study by numerically investigating the scattering by a cylindrical barrier intersecting the liquid surface through a pinned contact line. Detailed numerical simulations of potential flow coupled with the surface elevation dynamics were conducted to analyze the interactions between the wave and the barrier. Parameters such as wave frequency and barrier radius were varied to examine their effects on the scattering. The results highlight how the barrier's dimensionless size and the Bond number influence the scattering, with notable findings on the dependency of the scattering efficiency on these parameters. The study elucidates the role of contact lines and barrier size in modifying the scattering and presents a comprehensive view of the scattering across different parameter ranges.
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- Award ID(s):
- 2306106
- PAR ID:
- 10609238
- Publisher / Repository:
- 77th Annual Meeting of the Division of Fluid Dynamics
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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