WATER WAVE SCATTERING BY A VERTICAL POROUS BARRIER WITH TWO GAPS

2019 ◽  
Vol 61 (1) ◽  
pp. 47-63 ◽  
Author(s):  
M. SIVANESAN ◽  
S. R. MANAM
Keyword(s):  
Water Wave ◽  
Wave Scattering ◽  
Original Problem ◽  
Analytical Procedure ◽  
Explicit Solutions ◽  
Scattering Problems ◽  
Geometrical Structures ◽  
Water Wave Scattering ◽  
Weakly Singular ◽  
Porous Barrier

Explicit solutions are rarely available for water wave scattering problems. An analytical procedure is presented here to solve the boundary value problem associated with wave scattering by a complete vertical porous barrier with two gaps in it. The original problem is decomposed into four problems involving vertical solid barriers. The decomposed problems are solved analytically by using a weakly singular integral equation. Explicit expressions are obtained for the scattering amplitudes and numerical results are presented. The results obtained can be used as a benchmark for other wave scattering problems involving complex geometrical structures.

scholarly journals Accurate Solutions to Water Wave Scattering by Vertical Thin Porous Barriers

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Ai-jun Li ◽  
Yong Liu ◽  
Hua-jun Li
Keyword(s):  
Water Wave ◽  
Wave Scattering ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Wave Interaction ◽  
Wave Forces ◽  
Pressure Jump ◽  
Water Wave Scattering ◽  
Porous Barrier ◽  
Porous Barriers

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.

scholarly journals Dual integral equations—revisited

2003 ◽  
Vol 2003 (17) ◽  
pp. 1093-1100
Author(s):  
Sudeshna Banerjea ◽  
C. C. Kar
Keyword(s):  
Exact Solution ◽  
Integral Equations ◽  
Water Wave ◽  
Wave Scattering ◽  
Dual Integral Equations ◽  
Scattering Problems ◽  
End Points ◽  
Water Wave Scattering ◽  
The One

Dual integral equations with trigonometric kernel are reinvestigated here for a solution. The behaviour of one of the integrals at the end points of the interval complementary to the one in which it is defined plays the key role in determining the solution of the dual integral equations. The solution of the dual integral equations is then applied to find an exact solution of the water wave scattering problems.

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