arXiv subjects

Yong Sung Park

Publications and source records attributed to Yong Sung Park.

3 recordsLinked to original sources

arXiv2026

Wave scattering around a submerged vertical 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 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 $\varepsilon_{\max}(kb)$ 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.

physics.flu-dyn↗

arXiv2026

Exact linearisation of the nonlinear shallow-water equations over a moving bottom: classification, wave generation and run-up

The Carrier--Greenspan hodograph transformation linearises the nonlinear shallow-water equations on a beach of constant slope. We extend the transformation to a moving bottom and identify the family of bottom motions that preserves the Carrier--Greenspan invariants. The bottom gradient must be uniform in space, that is, $h(x,t)=ρ(t)x+\mathcal{B}(t)$, and constant $ρ$ returns the classical slope. For this family a horizontally accelerating frame removes the forcing. The bottom motion then disappears from the hodograph equation, and two quadratures recover the physical variables. If the gradient varies in time, the bed displacement grows without bound offshore and the far field cannot remain at rest. The domain must therefore be finite, although the pivot may be placed anywhere. A bottom-tilting wave maker realises this family. Closed forms follow for the hinge response, for the crest-to-trough steepness of the generated wave, and for the leading nonlinear correction. The correction depends on the point to which the steepness is referred, and so differs between a leading-elevation and a leading-depression wave. Because the hinge is at the beach toe, these closed forms provide the incident wave required by the classical plane-beach solution. The run-up can therefore be predicted from the plate motion alone. The steepness is predicted without a fitted constant and agrees with the reference computations. Sixty-one runs over a level bed, reported here for the first time, carry the test to deeper water and longer plate motions. The measured run-up follows the predicted run-up, with an offset that the inviscid theory does not account for.

physics.flu-dyn↗

arXiv2026

A floor and a ceiling for the advancing contact angle

Reported maxima of the advancing contact angle scatter from $87^\circ$ to $147^\circ$ in a single systematic study, and liquids on surfaces with static angles as low as $5^\circ$ reach dynamic maxima near $90^\circ$. We show that both observations follow from the hinged motion of the free surface near a moving contact line. The local Stokes solution for a wedge rotating about its contact line has two singular angles of opposite character: at $90^\circ$ the hinged motion generates no wall shear and the rotation is free, and at $θ_h = 128.73^\circ$, where $\tan 2α= 2α$, a resonance with the $r^2$ eigensolution arrests the rotation through an $r^2 \ln r$ term. Between the two angles lies a band that a transient advancing angle cannot leave while the interface near the contact line remains a quasi-steady wedge. A compilation of 68 liquid-solid systems from nine sources and five configurations confirms the band and its two exits: systems not limited by the apparatus, with $θ_s \le 40^\circ$, reach $87^\circ$ to $119^\circ$ regardless of chemistry, and every exceedance of $θ_h$ occurs either where chemistry places the static angle above the band or where the flow leaves the quasi-steady regime. The record of a waterline on a vertical wall exhibits the band within a single unsteady experiment, together with a distinct quieting of the local contact angle at the crossing of $90^\circ$.

cond-mat.soft↗