Wave scattering around a submerged vertical permeable breakwater

@misc{kim2026wave,
  title = {{Wave scattering around a submerged vertical permeable breakwater}},
  author = {Jeongin Kim and Yong Sung Park},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.06089},
  eprint = {2608.06089},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.06089},
  note = {CC BY-NC-ND 4.0},
}

TY  - UNPB
TI  - Wave scattering around a submerged vertical permeable breakwater
AU  - Jeongin Kim
AU  - Yong Sung Park
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2608.06089
UR  - https://arxiv.org/abs/2608.06089
AB  - An analytical solution for a wave velocity field scattered by a submerged permeable vertical plate-type breakwater under the linear monochromatic wave is obtained and the applications of the solution are presented. The water has an infinite depth, and the flow is assumed to be incompressible, inviscid, and irrotational, which leads to the two-dimensional potential wave theory. The permeable breakwater vertically occupies a finite interval beneath the water surface and the water flows through the breakwater. The porous boundary condition is linear, but it couples the normal velocity on the plate to the discontinuity in the velocity potential across it, so that the scattering problem does not reduce directly to a Riemann-Hilbert problem of standard form. This is resolved by a perturbation expansion in a small dimensionless parameter representing the permeability. The solution is expanded up to the first order: the leading order gives the wave scattered by the impermeable breakwater through a homogeneous Riemann-Hilbert problem, and the first-order term gives the correction for the permeability through a nonhomogeneous Riemann-Hilbert problem. The far-field amplitudes follow in closed form up to a single Cauchy principal-value integral. The effects of wavelength, breakwater length, and breakwater permeability conditions on the reflection and transmission coefficients are discussed in detail as an illustrative example of the application of the solution. An exact energy identity is also derived; it verifies the first-order solution and yields a closed-form energy-consistency bound ε_max(kb) on the perturbation parameter, beyond which the truncated expansion ceases to conserve energy. The hydrodynamic load on the plate is obtained to the same order, and the leading-order results are verified against the closed-form solution of Evans for the impermeable plate.
ER  -