Abstract
The Bragg reflections of oblique water waves by periodic surface-piercing structures over periodic bottoms are investigated using the eigenfunction matching method (EMM). Based on the assumption of small wave amplitude, the linear wave theory is employed in the solution procedure. In the step approximation, the surface-piercing structures and the bottom profiles are sliced into shelves separated by abrupt steps. For each shelf, the solution is composed of eigenfunctions with unknown coefficients representing the wave amplitudes. Upon applying the conservations of mass and momentum, a system of linear equations is obtained and is then solved by a sparse-matrix solver. The proposed EMM is validated by several examples in the literature. Then, the method is applied to solve Bragg reflections of oblique water waves by various surface-piercing structures over periodic bottoms. From the numerical experiments, Bragg’s law of oblique waves was used to predict the occurrences of Bragg resonance.
Highlights
When wind waves generated in the deep-water approach coastal regions, they experience various physical phenomena caused by inferences with structures, bathymetric variations, nonlinear wave interactions, etc
It is interesting to observe that a larger incidence angle results in a less intensive Bragg reflection and the primary resonance 2S(cos α)/λ = 1 is stronger than the secondary resonance 2S(cos α)/λ = 2, which are totally opposite to the situations of Bragg reflections caused solely by periodic surface-piercing structures
The surface-piercing structures and bottom profiles are sliced into a number of shelves separated by abrupt steps
Summary
When wind waves generated in the deep-water approach coastal regions, they experience various physical phenomena caused by inferences with structures, bathymetric variations, nonlinear wave interactions, etc. Manisha et al [47] recently developed a model considering the effects of bottom undulations for oblique wave interaction with a surface-piercing rectangular structure behind a submerged breakwater or a trench. They connected the solutions of the MSE and EMM for the regions of the undulated bottom and rectangular structure over the flat bottom, respectively. The EMM model is developed for analyzing the combined phenomena of oblique incidence, surface-piercing structures of different shapes, Bragg reflections, and undulated bottoms.
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