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Research Papers: Ocean Engineering

Propagation of Gravity Waves Past Multiple Bottom-Standing Barriers

[+] Author and Article Information
D. Karmakar

Centre for Marine Technology and Engineering,
Instituto Superior Técnico,
Universidade de Lisboa,
Av. Rovisco Pais,
1049-001 Lisboa, Portugal
e-mail: debabrata.karmakar@centec.tecnico.ulisboa.pt

C. Guedes Soares

Fellow ASME
Centre for Marine Technology and Engineering,
Instituto Superior Técnico,
Universidade de Lisboa,
Av. Rovisco Pais,
1049-001 Lisboa, Portugal
e-mail: c.guedes.soares@centec.tecnico.ulisboa.pt

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received October 26, 2013; final manuscript received June 8, 2014; published online October 6, 2014. Assoc. Editor: Celso P. Pesce.

J. Offshore Mech. Arct. Eng 137(1), 011101 (Oct 06, 2014) (10 pages) Paper No: OMAE-13-1102; doi: 10.1115/1.4027896 History: Received October 26, 2013; Revised June 08, 2014

The interaction of oblique surface gravity waves with multiple bottom-standing flexible porous breakwaters is analyzed based on the linearized theory of water waves. Using the method of eigenfunction expansion and the least square approximation, the wave propagation in the presence of single bottom-standing barriers is analyzed considering the upper edge to be: (i) free and (ii) moored, whereas the lower edge is considered to be clamped at the bottom. The wide-spacing approximation is used to analyze the wave interaction with multiple porous bottom-standing flexible barriers to understand the effect of the submerged flexible barriers as an effective breakwater. A brief comparison of both the upper edge conditions is carried out to analyze the effect of wave dissipation due to the presence of multiple barriers. The numerical results for the reflection and transmission coefficients along with the free surface vertical deflection are obtained for the case of two and three multiple bottom-standing barriers. The attenuation in the wave height due to the presence of porosity, change in barrier depth, and distance between the barriers are analyzed. The present study will be helpful in the analysis of proper functioning of porous bottom-standing barrier as an effective breakwater for the protection of offshore structures.

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Figures

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Fig. 1

Schematic diagram for multiple bottom-standing barriers

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Fig. 2

Schematic diagram for single bottom-standing barrier

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Fig. 3

Kr and Kt versus γ0h for various values of barrier height d/h with G = 1.0 + i and a/h = 0.05 in the case of free-clamped double barrier

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Fig. 4

Kr and Kt versus γ0h for various values of porosity effect parameter G with d/h = 0.1 and a/h = 0.05 in the case of free-clamped double barrier

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Fig. 5

Kr and Kt versus γ0h for various values of distance of the barrier L/h with d/h = 0.1 and G = 1.0 + i in the case of free-clamped triple barrier

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Fig. 6

Kr and Kt versus γ0h for various values of barrier depth d/h with G = 1.0 + i and a/h = 0.05 in the case of moored-clamped double barrier

Grahic Jump Location
Fig. 7

Kr and Kt versus γ0h for various values of porosity effect parameter G with d/h = 0.1 and a/h = 0.05 in the case of moored-clamped double barrier

Grahic Jump Location
Fig. 8

Kr and Kt versus γ0h for various values of distance of the barrier L/h with d/h = 0.1 and G = 1.0 + i in the case of moored-clamped double barrier

Grahic Jump Location
Fig. 9

Kr and Kt versus γ0h for various values of distance of the barrier L/h with d/h = 0.1 and G = 1.0 + i in the case of moored-clamped triple barrier

Grahic Jump Location
Fig. 10

ζj(x,t) versus distance x for various values of porosity effect parameter G with γ0h = 3.0, a/h = 0.05, and d/h = 0.1 in the case of free-clamped double barrier

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Fig. 11

ζj(x,t) versus distance x for various values of barrier depth d/h with γ0h = 3.0, a/h = 0.05, and G = 1.0 + i in the case of free-clamped triple barrier

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Fig. 12

ζj(x,t) versus distance x for various values of porosity effect parameter G with γ0h = 3.0, a/h = 0.05, and d/h = 0.1 in the case of free-clamped triple barrier

Grahic Jump Location
Fig. 13

ζj(x,t) versus distance x for various values of porosity effect parameter G with γ0h = 3.0, a/h = 0.05, and d/h = 0.1 in the case of moored-clamped double barrier

Grahic Jump Location
Fig. 14

ζj(x,t) versus distance x for various values of barrier depth d/h with γ0h = 3.0, a/h = 0.05, and G = 1.0 + i in the case of moored-clamped triple barrier

Grahic Jump Location
Fig. 15

ζj(x,t) versus distance x for various values of porosity effect parameter G with γ0h = 3.0, a/h = 0.05, and d/h = 0.1 in the case of moored-clamped triple barrier

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