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TECHNICAL PAPERS

Scattering of Surface and Internal Waves by Rectangular Dikes

[+] Author and Article Information
P. Suresh Kumar1

Coastal Engineering Research Department, Korea Ocean Research and Development Institute, Ansan P.O. Box 29, Seoul 425-600, Koreasuresẖbbsr2000@yahoo.com

J. Bhattacharjee, T. Sahoo

Department of Ocean Engineering and Naval Architecture, Indian Institute of Technology Kharagpur, Kharagpur 721302, India

1

Corresponding author.

J. Offshore Mech. Arct. Eng 129(4), 306-317 (Apr 28, 2007) (12 pages) doi:10.1115/1.2786473 History: Received December 17, 2006; Revised April 28, 2007

The scattering of surface and internal waves by a single dike or a pair of identical dikes in a two-layer fluid is analyzed in two dimensions within the context of linearized theory of water waves. The dikes are approximated as cylinders of rectangular geometry and are placed in a two-layer fluid of finite depth. In the study, both the cases of surface-piercing and bottom-standing dikes are considered. The solution of the associated boundary value problem is derived by a matched eigenfunction expansion method. Because of the flow discontinuity at the interface, the eigenfunctions involved have an integrable singularity at the interface and the orthonormal relation used in the present analysis is a generalization of the classical one corresponding to a single-layer fluid. The reflection coefficients and force amplitudes are computed and analyzed in various cases. The computed results in a two-layer fluid are compared with those existing in the literature for a single-layer fluid. The results obtained by the matched eigenfunction expansion method are compared with that of wide-spacing approximation method, and it is observed that the results from both the methods are in good agreement when the dikes are widely spaced. The general behavior of reflection coefficients for interface-piercing and non-interface-piercing obstacles is found to be different in both cases of surface-piercing and bottom-standing dikes. Moreover, for surface-piercing dikes, the results show the possibility of very large resonant motions between the dikes but with a very narrow bandwidth for the frequency of interest.

Copyright © 2007 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Definition sketch for a single surface-piercing dike

Grahic Jump Location
Figure 2

Definition sketch for a pair of identical surface-piercing dikes

Grahic Jump Location
Figure 3

Definition sketch for a single bottom-standing dike

Grahic Jump Location
Figure 5

Comparison of reflection coefficients in SM, KrI and IM, KrII versus pId for a single surface-piercing dike at different H∕d values, a∕d=1.0, h∕H=0.25, and s=0.75 with Mei and Black (3)

Grahic Jump Location
Figure 6

Reflection coefficients in (a) SM, KrI and (b) IM, KrII versus pId for a single surface-piercing dike at different H∕d values, a∕d=1.0, h∕H=0.25, and s=0.75

Grahic Jump Location
Figure 7

Reflection coefficients in (a) SM, KrI and (b) IM, KrII versus pId for a single surface-piercing dike at different a∕d values, H∕d=6.0, h∕H=0.25, and s=0.75

Grahic Jump Location
Figure 8

Reflection coefficients in (a) SM, KrI and (b) IM, KrII versus pId for a single surface-piercing dike at different h∕H values, H∕d=5.0, a∕d=1.0, and s=0.75

Grahic Jump Location
Figure 9

Reflection coefficients in (a) SM, KrI and (b) IM, KrII versus pId for a single surface-piercing dike at different s values, H∕d=5.0, a∕d=1.0, and h∕H=0.25

Grahic Jump Location
Figure 10

Reflection coefficients in (a) SM, KrI and (b) IM, KrII versus pId for a pair of identical surface-piercing dikes at different b∕H values, H∕d=6.0, a∕d=1.0, s=0.75, and h∕H=0.25

Grahic Jump Location
Figure 11

(a) Horizontal force and (b) vertical force per unit incident wave amplitude and length of dike in MN∕m2 for a single surface-piercing dike at different H∕d values, a∕d=1.0, s=0.75, and h∕H=0.25

Grahic Jump Location
Figure 12

(a) Horizontal force and (b) vertical force per unit incident wave amplitude and length of dike in MN∕m2 for a single surface-piercing dike at different a∕d values, H∕d=6.0, s=0.75, and h∕H=0.25

Grahic Jump Location
Figure 13

Horizontal force on the first, ∣HF1∕I0∣, and second, ∣HF2∕I0∣, dikes in MN∕m2 for (a) b∕H=0.25 and (b) b∕H=0.75 at H∕d=6.0, a∕d=0.1, s=0.75, and h∕H=0.25

Grahic Jump Location
Figure 14

Vertical force on the first, ∣VF1∕I0∣, and second, ∣VF2∕I0∣, dikes in MN∕m2 for (a) b∕H=0.25 and (b) b∕H=0.75 at H∕d=6.0, a∕d=0.1, s=0.75, and h∕H=0.25

Grahic Jump Location
Figure 18

Reflection coefficients in (a) SM,KrI and (b) IM, KrII versus pI(H−d) for a single bottom-standing dike at different s values, H∕d=2.0, a∕d=6.0, and h∕H=0.25

Grahic Jump Location
Figure 19

Reflection coefficients in (a) SM, KrI and (b) IM, KrII versus pI(H−d) for a pair of identical bottom-standing dikes at different b∕H values, H∕d=2.0, a∕d=6.0, s=0.75, and h∕H=0.25

Grahic Jump Location
Figure 4

Definition sketch for a pair of identical bottom-standing dikes

Grahic Jump Location
Figure 17

Reflection coefficients in (a) SM, KrI and (b) IM, KrII versus pI(H−d) for a single bottom-standing dike at different h∕H values, H∕d=2.0, a∕d=6.0, and s=0.75

Grahic Jump Location
Figure 16

Reflection coefficients in (a) SM, KrI and (b) IM, KrII versus pI(H−d) for a single bottom-standing dike at different a∕d values, H∕d=2.0, h∕H=0.25, and s=0.75

Grahic Jump Location
Figure 15

Reflection coefficients in (a) SM, KrI and (b) IM, KrII versus pI(H−d) for a single bottom-standing dike at different H∕d values, a∕d=6.0, h∕H=0.25, and s=0.75

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