Oblique wave scattering by a semi-infinite elastic plate with finite draft floating on a step topography

On the basis of a potential theory and Euler-Bernoulli beam theory, an analytical solution for oblique wave scattering by a semi-infinite elastic plate with finite draft floating on a step topography is developed using matched eigenfunction expansions. Different from previous studies, the effects of a wave incident angle, a plate draft, three different plate edge conditions （free, simply supported and built-in） and a sea-bottom topography are all taken into account. Moreover, the plate edge conditions are directly incorporated into linear algebraic equations for determining unknown expansion coefficients in velocity potentials, which leads to a simple and efficient solving procedure. Numerical results show that the convergence of the present solution is good, and an energy conservation relation is well satisfied. Also, the present predictions are in good agreement with known results for special cases. The effects of the wave incident angle, the plate draft, the plate edge conditions and the sea-bottom topography on various hydrodynamic quantities are analyzed. Some useful results are presented for engineering designs.

Scattering of Oblique Water Waves by Two Unequal Surface-Piercing Vertical Thin Plates with Stepped Bottom Topography

Based on linear water-wave theory, this study investigated the scattering of oblique incident water waves by two unequal surface-piercing thin vertical rigid plates with stepped bottom topography. By using the matched eigenfunction expansion method and a least square approach, the analytical solutions are sought for the established boundary value problem. The effects of the incidence angle, location of step, depth ratio of deep to shallow waters,and column width between two plates, on the reflection coefficients, the horizontal wave forces acting on the two plates, and the mean surface elevation between the two plates, are numerically examined under a variety of wave conditions. The results show that the existence of the stepped bottom between two plates considerably impacts the hydrodynamic performances of the present system. It is found that the effect of stepped bottom on the reflection coefficient of the present two-plate structure is evident only with waves of the low dimensionless frequency.Moreover, the influence of the step location on the hydrodynamic performance of the present two-plate structure is slight if the step is placed in between the two plates.

CONJUGATE FLOWS OVER A STEP IN A THREE-LAYER FLUID

The conjugate flows over a step with the height h_0, which might be positive or negative, was studied in a three-layer fluid and the coupled nonlinear equations were derived, with which the effects of varying height h_0 on the existence and evolution of conjugate flows were examined. It is concluded that the conjugate flow is sharply sensitive to the thickness of fluid layers and its characteristics alters remarkably due to the existence of the step. As the flow climbs up a step (h_0>0), the conjugate flow with a convex lower interface and a concave upper interface is allowed to appear, while the flow with the concave lower interface or the simultaneous concave interfaces will be depressed. As the flow goes down a step (i.e., h_0<0), on most occasions only one kind of conjugate flow could exist, which prossesses the form with the simultaneous convex interfaces and will disappear rapidly with the increase of the step depth.