2026 Kim Submerged Permeable Breakwater

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 resulting nonlinear boundary condition is resolved by the perturbation method with a small parameter representing the permeability. The solution was expanded up to the first order so that the leading-order term can represent the wave scattered by the impermeable breakwater and the first-order term can give the correction to the solution considering the wave scattered by the permeable breakwater. Each order of the wave velocity potential is determined by a reduction method and this leads to the homogeneous Riemann-Hilbert problem for the leading-order problem and the nonhomogeneous Riemann-Hilbert problem for the first-order problem. 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 boundary of the validity range of the expansion.