ABSTRACT

The present work is concerned with the interaction of oblique surface gravity waves by a simple and composite porous block of finite width placed on a multi-step bottom in a two-layer fluid. The ocean depth is taken to be finite and its bed impermeable. The problem is studied by employing linearised water wave theory and eigenfunction expansion. The dispersion relations and their roots are analysed which give a clear understanding of the phenomenon. The cases of simple and composite interface-piercing structures are taken up separately to investigate the impact of porosity in wave attenuation for surface and interface modes. Waves propagate through the porous structure with distinct eigenvalues. The appropriateness of structures of various configurations on the scattering of surface waves is investigated by examining the reflection coefficients for waves in surface and interface modes as well as their effects on the free surface and interface elevations, the wave-loads on the structure and the rigid wall supporting the structure at one end. Further, as a special case, the sea-bed preceding the step bottom is considered to be porous and its effect on reflection is examined. The investigation establishes that for a suitable configuration of the porous structure, an optimum width can be ascertained to design a breakwater of reasonable efficiency possessing characteristics of both reflection and dissipation processes. The problems are solved analytically and the results are presented in graphical form. This kind of study is likely to have immense significance for designing of different types of coastal structures with respect to reflection and dissipation of wave energy at continental shelves which is influenced by a stratified fluid, which is modelled in this work as a two-layer fluid for convenience. Comparison of present results with available results show good agreement and this points towards the effectiveness of the model described in this work.

摘要

目前的工作涉及倾斜表面重力波与有限宽度的简单复合多孔块的相互作用，该多孔块放置在两层流体中的多级底部。海洋深度被认为是有限的，它的海床是不可渗透的。通过采用线性化水波理论和特征函数展开来研究该问题。分析了色散关系及其根源，从而清楚地了解了这一现象。分别以简单和复合的界面穿透结构为例，研究孔隙度对表面和界面模式波衰减的影响。波通过具有不同特征值的多孔结构传播。通过研究表面和界面模式中波的反射系数及其对自由表面和界面高程、结构上的波载荷和刚体的影响，研究了各种结构对表面波散射的适用性在一端支撑结构的墙。此外，作为一种特殊情况，阶梯底部之前的海床被认为是多孔的，并检查了其对反射的影响。研究表明，对于多孔结构的合适配置，可以确定最佳宽度，以设计具有反射和耗散过程特征的具有合理效率的防波堤。分析解决了这些问题，并以图形形式显示了结果。这种研究可能对设计不同类型的海岸结构具有重要意义为了方便。当前结果与可用结果的比较显示出良好的一致性，这表明本工作中描述的模型的有效性。