Abstract
In this paper, we investigate wave attenuation caused by mangroves as a porous media. A 1-D mathematical model is derived by modifying the shallow water equations (SWEs). Two approaches are used to involve the existing of mangrove: friction term and diffusion term. The model will be solved analytically using the separation of variables method and numerically using a staggered finite volume method. From both methods, wave transmission coefficient will be obtained and used to observe the damping effect induced by the porous media. Several comparisons are shown to examine the accuracy and robustness of the derived numerical scheme. The results show that the friction coefficient, diffusion coefficient and vegetation’s length have a significant effect on the transmission coefficient. Moreover, numerical observation is extended to a 2-D SWEs, where we conduct a numerical simulation over a real bathymetry profile. The results from the 2-D numerical scheme will be validated using the data obtained from the field measurement which took place in Demak, Central Java, Indonesia. The results from this research will be beneficial to determine the characteristics of porous structures used for coastal protection.
Highlights
The ocean covers 71% of the Earth’s surface and 40% of the world population, approximately 2.4 billion people, live within 100 km of the coast
The mathematical models will be derived based on shallow water equations (SWEs) to represent the wave attenuation caused by the porous media
We can conclude that the wave attenuation factors are friction coefficient c f, diffusion coefficient cD, and vegetation length
Summary
The ocean covers 71% of the Earth’s surface and 40% of the world population, approximately 2.4 billion people, live within 100 km of the coast. The phenomenon of wave amplitude reduction by porous media, vegetation, or in this case, mangroves, have been studied using numerous models [28–40]. We aim to provide a new alternative simpler model to approximate wave attenuation caused by porous media that is numerically less expensive, yet, still quite accurate. In this research, we propose a model to study the mechanism of the phenomenon even further by involving multiple porous media and using a real bathymetry profile of a beach in Demak, analytically and numerically. The mathematical models will be derived based on shallow water equations (SWEs) to represent the wave attenuation caused by the porous media. The SWEs can be a very effective alternative model to be applied in the future works relating to this field This has been confirmed by several researchers who have applied shallow water equations to many cases of wave modelling [44–52]. Section six will conclude this paper and give some recommendations for future researches
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