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The Diffraction of Multidirectional Random Waves by Rectangular Submarine Pits

[+] Author and Article Information
Hong Sik Lee

Department of Civil Engineering, Chung-Ang University, Anseong, Gyeonggi-Do, 456-756, South Korea

A. Neil Williams

Department of Civil and Environmental Engineering, University of Houston, Houston, TX, 77204-4791, USA

J. Offshore Mech. Arct. Eng 126(1), 9-15 (Mar 02, 2004) (7 pages) doi:10.1115/1.1641387 History: Received August 01, 2002; Revised May 01, 2003; Online March 02, 2004
Copyright © 2004 by ASME
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References

Newman,  J. N., 1965, “Propagation of Water Waves Over an Infinite Step,” J. Fluid Mech., 23, pp. 399–415.
Hilaly,  N., 1969, “Water Waves Over a Rectangular Channel Though a Reef,” J. Waterw. Harbors Div., Am. Soc. Civ. Eng., 95, pp. 77–94.
Lee,  J. J., and Ayer,  R. M., 1981, “Wave Propagation Over a Rectangular Trench,” J. Fluid Mech., 110, pp. 335–347.
Miles,  J. W., 1982, “On Surface Wave Diffraction by a Trench,” J. Fluid Mech., 115, pp. 315–325.
Kirby,  J. T., and Dalrymple,  R. A., 1983, “Propagation of Obliquely Incident Water Waves Over a Trench,” J. Fluid Mech., 133, pp. 47–63.
Ting,  C. K. F., and Raichlen,  F., 1986, “Wave Interaction With a Rectangular Trench,” J. Waterw., Port, Coastal, Ocean Eng., 112, pp. 454–460.
Kirby,  J. T., Dalrymple,  R. A., and Seo,  S. N., 1987, “Propagation of Obliquely Incident Water Waves Over a Trench. Part 2. Current Flowing Along the Trench,” J. Fluid Mech., 176, pp. 95–116.
Williams,  A. N., 1990, “Diffraction of Long Waves by Rectangular Pit,” J. Waterw., Port, Coastal, Ocean Eng., 116, pp. 459–469.
McDougal,  W. G., Williams,  A. N., and Furukawa,  K., 1996, “Multiple-Pit Breakwaters,” J. Waterw., Port, Coastal, Ocean Eng., 122, pp. 27–33.
Williams,  A. N., and Vazquez,  J. H., 1991, “Wave Interaction With a Rectangular Pit,” ASME J. Offshore Mech. Arct. Eng., 113, pp. 193–198.
Goda, Y., 1985, “Random Seas and Design of Maritime Structures,” Univ. of Tokyo Press.
Mitsuyasu,  H., Tasai,  F., Suhara,  T., Mizuno,  S., Ohkusu,  M., Honda,  T., and Rikiishi,  K., 1975, “Observation of the Directional Spectrum of Ocean Waves Using a Cloverleaf Buoy,” J. Phys. Oceanogr., 5, pp. 750–760.

Figures

Grahic Jump Location
Definition sketch for multiple-pit configuration
Grahic Jump Location
Contour maps of diffraction coefficients for a single pit with b/a=1.0(a=6 m,b=6 m), k1d=π/10,k2h=π/10√2,h/d=0.5(h=1.5 m,d=3.0 m), θ=θR=0°,a/d=2.0,T=T1/3=11 s,L=L1/3=42.46 m, for (a) regular waves, (b) random waves with Smax=10
Grahic Jump Location
Contour maps of diffraction coefficients for a single pit with b/a=0.1(a=1000 m,b=100 m), h/d=0.5(h=6 m,d=12 m), kh=0.269,θ=θR=0°,T=T1/3=18 s,L=L1/3=140.15 m, for (a) regular waves, (b) random waves with Smax=10
Grahic Jump Location
Contour maps of diffraction coefficients for a dual pit configuration with bj/aj=2.0(aj=19 m,bj=38 m;j=1, 2), d/h=3.0(d=3 m,h=1 m), kh=0.167,θ=θR=0°,T=T1/3=12 s,L=L1/3=37.5 m, for (a) regular waves, (b) random waves with Smax=10. The edge-to-edge pit spacing is 38 m
Grahic Jump Location
Contour maps of diffraction coefficients for a triple pit configuration with bj/aj=2.0(aj=19 m,bj=38 m;j=1,2,3),d/h=3.0(d=3 m,h=1 m), kh=0.167,θ=θR=0°,T=T1/3=12 s,L=L1/3=37.5 m, for (a) regular waves, (b) random waves with Smax=10. The edge-to-edge pit spacing is 38 m
Grahic Jump Location
Contour maps of diffraction coefficients for a dual pit configuration with b1/a1=4.0(a1=38 m,b1=152 m), b2/a2=0.1(a2=1000 m,b2=100 m), h/d=0.5(h=6 m,d=12 m), kh=0.269,θ=θR=0°,T=T1/3=18 s,L=L1/3=140.15 m, for (a) regular waves, (b) random waves with Smax=10. The edge-to-edge pit spacing is 462 m
Grahic Jump Location
Contour map of diffraction coefficient for a single pit with b/a=0.1(a=1000 m,b=100 m), h/d=0.5(h=6 m,d=12 m), kh=0.269,θR=0°,T1/3=18 s,L1/3=140.15 m for random waves with Smax=75
Grahic Jump Location
Contour map of diffraction coefficient for a dual pit configuration with bj/aj=2.0(aj=19 m,bj=38 m;j=1,2),d/h=3.0(d=3 m,h=1 m), kh=0.167,θR=0°,T1/3=12 s,L1/3=37.5 m for random waves with Smax=75. The edge-to-edge pit spacing is 38 m
Grahic Jump Location
Contour map of diffraction coefficient for a triple pit configuration with bj/aj=2.0(aj=19 m,bj=38 m;j=1,2,3),d/h=3.0(d=3 m,h=1 m), kh=0.167,θR=0°,T1/3=12 s,L1/3=37.5 m for random waves with Smax=75. The edge-to-edge pit spacing is 38 m
Grahic Jump Location
Contour map and diffraction coefficient for a dual pit configuration with b1/a1=4.0(a1=38 m,b1=152 m), b2/a2=0.1(a2=1000 m,b2=100 m), h/d=0.5(h=6 m,d=12 m), kh=0.269,θR=0°,T1/3=18 s,L1/3=140.15 m for random waves with Smax=75. The edge-to-edge pit spacing is 462 m
Grahic Jump Location
Contour maps of diffraction coefficients for the same pit configurations as Figs. 78910 (or Figs. 3456), but with Smax=25
Grahic Jump Location
Variation of maximum and minimum diffraction coefficient with (a) dimensionless pit width, b/L=b/L1/3, for a/L=a/L1/3=0.5,d/h=3.0kh=0.167,θ=θR=0°; (b) dimensionless pit length, a/L=a/L1/3, for b/L=b/L1/3=1.0,d/h=3.0,kh=0.167,θ=θR=0°; (c) dimensionless pit depth, d/h, for a/L=a/L1/3=0.5,b/L=b/L1/3=1.0,kh=0.167,θ=θR=0°; and (d) angle of incidence θ=θR for a/L=a/L1/3=0.5,b/L=b/L1/3=1.0,d/h=3.0,kh=0.167. Notations: minimum diffraction coefficient for regular waves (▪▪▪); (•••) random waves with Smax=10, (▴▴▴) random waves with Smax=75; maximum diffraction coefficient-same symbols as minimum but without fill

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