Abstract
The water wave scattering by vertical thin porous barriers is accurately solved in this study. Two typical structures of a surface-piercing barrier and a submerged bottom-standing barrier are considered. The solution procedure is based on the multi-term Galerkin method, in which the pressure jump across a porous barrier is expanded in a set of basis functions involving the Chebychev polynomials. Then, the square-root singularity of fluid velocity at the edge of the porous barrier is correctly modeled. The present solutions have the merits of very rapid convergence. Accurate results for both the reflection and the transmission coefficients and wave forces are presented. This study not only gives a promising procedure to tackle wave interaction with vertical thin porous barriers but also provides a reliable benchmark for complicated numerical solutions.
Highlights
Vertical thin plates have been used as simple breakwaters in coastal engineering due to their merits of simple structure, constructing convenience, and low engineering cost
The two approaches based on expanding the pressure jump at D and the fluid velocity at Λ for solid barrier can give the lower and upper bounds of hydrodynamic quantities, respectively
This study has developed accurate solutions for water wave scattering by two types of thin vertical porous barriers based on the linear potential theory
Summary
Vertical thin plates have been used as simple breakwaters in coastal engineering due to their merits of simple structure, constructing convenience, and low engineering cost. Losada et al [9] and Abul-Azm [10] used matched eigenfunction expansion method to develop analytical solutions for obliquely and normally incident wave scattering by vertical thin barriers with different configurations, respectively. Porter and Evans [1] investigated oblique wave scattering by various partial solid barriers using a multiterm Galerkin method and obtained the upper and lower boundaries of reflection and transmission coefficients with extremely high accuracy. Banerjea et al [12] used the multi-term Galerkin method to obtain accurate solutions for oblique wave scattering by single and double submerged vertical solid barriers with gaps. Compared with matched eigenfunction expansion method, the beauty of multi-term Galerkin method is that it can correctly model the squareroot singularity of fluid velocity near the edge of vertical plate. Extremely accurate results of hydrodynamic quantities can be obtained
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