Elastic Bottom Effects on Ocean Water Wave Scattering by a Composite Caisson-Type Breakwater Placed Upon a Rock Foundation in a Two-Layer Fluid

The association of oblique surface gravity waves with a caisson-type multi-chamber porous breakwater fitted with a perforated front wall in a two-layer fluid is studied in finite ocean depth with an elastic bottom. This study focuses on the influence of porous parameters of the interface-piercing structure on wave attenuation in surface and interfacial modes. The flexural gravity wave motion establishes the influence of the elastic bottom. The reflection coefficients for waves in both modes are evaluated to show their effects on the free surface and interface elevations and the waveloads. Consequently, the appropriateness of various configurations of the structure on the wave scattering is studied. Due to wave dissipation by the structure, less waveload is detected on the stiff wall and less elevation is noticed in the porous zone. The structure’s multi-chamber division allows it to have more dissipative and reflective properties. Adjustment of the structure’s height, breadth, and porous parameter leads to achieving good amount of wave reflection and maximum energy dissipation. An optimal width can be determined for a suitable configuration of the structure so that a breakwater can be built with an acceptable level of reflection and dissipation characteristics. The shear force and bottom deflection show how elastic parameters of the sea-floor affect wave scattering.

Shallow water theory for structured bathymetry

A shallow water theory is developed which applies to surface wave propagation over structured bathymetry comprising rapid abrupt fluctuations in depth between two smoothly varying levels. Using a homogenization approach coupled to the depth-averaging process which underpins shallow water modelling, governing equations for the wave elevation are derived which explicitly relate local spatially varying anisotropy of wave speeds to properties of the microstructured bed. The model is applied to two water wave scattering problems both to demonstrate the complex wave propagation characteristics exhibited by structured beds and to provide examples of how to use structured beds to engineer bespoke wave propagation. This includes propagating waves with practically zero reflection and loss of form through circular bends in channels.

Step Approximation for Water Wave Scattering by Multiple Thin Barriers over Undulated Bottoms

This paper investigates the scattering of oblique water waves by multiple thin barriers over undulation bottoms using the eigenfunction matching method (EMM). In the solution procedures of the EMM, the bottom topographies are sliced into shelves separated by steps. On each step, surface-piercing or/and bottom-standing barriers can be presented or not. For each shelf, the solution is composed of eigenfunctions with unknown coefficients representing the wave amplitudes. Then applying the conservations of mass and momentum, a system of linear equations is resulted and can be solved by a sparse-matrix solver. If no barriers are presented on the steps, the proposed EMM formulation degenerates to the water wave scattering over undulating bottoms. The effects on the barrier lengths, barrier positions and oblique wave incidences by different undulated bottoms are studied. In addition, the EMM is also applied to solve the Bragg reflections of normal and oblique water waves by periodic barrier over sinusoidal bottoms. The accuracy of the solution is demonstrated by comparing it with the results in the literature.