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Wave Propagation 2011 Part 11

Tham khảo tài liệu 'wave propagation 2011 part 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | A Parabolic Equation for Wave Propagation over Porous Structures 287 gi kx cos 6 ky sin 6-a t ộ A x y where A x y is the amplitude of the velocity potential. From Eq. 31 we have 1 d 2ộ k 2 d 2 y ộ sin2 6 31 32 For full transmitted waves along the boundary Eq. 30 is reduced to Eq. 15 . In this model wave diffraction refraction reflection and breaking from porous structures were considered. The model is validated for wave propagating over a single cylindrical impermeable pile rest on a protecting cylindrical impermeable or permeable step. A typical case was performed by Hsu et al. 2009 . Fig. 13 presents the bathymetry of a single cylindrical pile rest on a protecting cylindrical step. The impermeable cylinder has a radius of ra L 4 and the radius of the cylindrical protection is rb L 2 where L is the wavelength. The wave incidence is equal to 45 . The incident wave height is H0 0.03 m . The results of analytical solutions presented by Silva et al. 2003 and predicted dimensionless wave amplitude fields are shown in Fig. 14. Fig. 15 shows the result of wave propagation over a single cylindrical impermeable pile on a protecting cylindrical permeable step n0 0.4 fp 1.0 . 1 y L 1 0 -1 2ỊỊ 0.1 0 -0.1 -0.2 -0.3 -2-10 1 2 x L y L Fig. 13. Bathymetry of a single cylindrical pile on a protecting cylindrical step In this two figures the compared profile is along the x L 0 and y L 0 axes. Comparing with theoretical results and present model it is clear that the numerical prediction is in good agreement with the analytical solution. The model is also applied to simulate wave transformation on a group of five vertical porous cylinders. Each cylinder has a radius L 4. In Fig. 16 the four cylinders are located at the vertices of a square of side dimension which is equal to 2L and the fifth one is located at the centre. The incident wave condition is the same with Fig.15. Fig. 17 shows the wave pattern for waves propagating over a group of five vertical permeable cylinders. The .