Wave analysis of porous geometry with linear resistance law

Abstract

The wave diffraction-radiation problem of a porous geometry of arbitrary shape located in the free surface of a fluid is formulated by a set of integral equations, assuming a linear resistance law at the geometry. The linear forces, the energy relation and the mean horizontal drift force are evaluated for non-porous and porous geometries. A geometry of large porosity has an almost vanishing added mass. The exciting forces are a factor of 5–20 smaller compared to a solid geometry. In the long wave regime, the porous geometry significantly enhances both the damping and the mean drift force, where the latter grows linearly with the wavenumber. The calculated mean drift force on a porous hemisphere and a vertical truncated cylinder, relevant to the construction of fish cages, is compared to available published results.

Keywords

wave analysis / fish cages / mean drift force / wave exciting force / added mass / damping

References

[1] An S, Faltinsen OM. Linear free-surface effects on a horizontally submerged and perforated 2D thin plate in finite and infinite water depths. Appl. Ocean Res., 2012, 37: 220-234

[2] Behera H, Koley S, Sahoo T. Wave transmission by partial porous structures in two-layer fluid. Engng. An. with Bound. Elements, 2015, 58: 58-78

[3] Chwang AT. A porous-wavemaker theory. J. Fluid Mech., 1983, 132: 395-406

[4] Chwang AT, Chan AT. Interaction between porous media and wave motion. Annu. Rev. Fluid Mech., 1998, 30: 53-84

[5] Chwang AT, Wu J. Wave scattering by submerged porous disk. J. Eng. Mech., 1994, 120: 2575-2587

[6] Faltinsen OM. Wave loads on offshore structures. Annu. Rev. Fluid Mech., 1990, 22: 35-56

[7] Finne S, Grue J. On the complete radiation-diffraction problem and wave-drift damping marine bodies in the yaw mode of motion. J. Fluid Mech., 1997, 357: 289-320

[8] Grue J, Biberg D. Wave forces on marine structures with small speed in water of restricted depth. Appl. Ocean Res., 1993, 15: 121-135

[9] Grue J, Palm E. The mean drift force and yaw moment on marine structures in waves and current. J. Fluid Mech., 1993, 250: 121-142

[10] Grue J, Palm E. Wave drift damping of floating bodies in slow yaw-motion. J. Fluid Mech., 1996, 319: 323-352

[11] Huang Z, Li Y, Liu Y. Hydraulic performance and wave loadings of perforated/slotted coastal structures: A review. Ocean Engng., 2011, 38: 10311053

[12] Jarlan GE. A perforated vertical wall break-water. Dock and Harb. Auth. XII, 1961, 486: 394-398

[13] Koley S, Kaligatla RB, Sahoo T. Oblique wave scattering by a vertical flexible porous plate. Stud. Appl. Math., 2015, 135: 134

[14] Koley S, Behera H, Sahoo T. Oblique wave trapping by porous structures near a wall. J. Engng. Mech., 2015, 141(3): 1-15

[15] Laws EM, Livsey JL. Flow through screens. Annu. Rev. Fluid Mech., 1978, 10: 247-266

[16] Liu Y, Li HJ. Wave reflection and transmission by porous breakwaters: a new analytical solution. Coast. Engng., 2013, 78: 4652

[17] Molin B. Second-order hydrodynamics applied to moored structures -A state-of-the-art survey. Ship Technology Res., 1994, 41: 59-84

[18] Molin B. On the added mass and damping of periodic arrays or partially porous disks. J. Fluids and Struct., 2001, 15: 275-290

[19] Molin B. Hydrodynamic modeling of perforated structures. Appl. Ocean Res., 2011, 33: 1-11

[20] Molin B, Remy F. Experimental and numerical study of the sloshing motion in a rectangular tank with a perforated screen. J. Fluids and Struct., 2013, 43: 463-480

[21] Newman JN, 1977. Marine hydrodynamics. MIT Press, 402.

[22] Newman JN. Cloaking a circular cylinder in water waves. Eur. J. Mech. B/Fluids, 2014, 47: 145-150

[23] Nossen J, Grue J, Palm E. Wave forces on three-dimensional floating bodies with small forward speed. J. Fluid Mech., 1991, 227: 135-160

[24] Taylor GI. Fluid flow in regions bounded by porous surfaces. Proc. Roy Soc. Lond. A, 1956, 234(1199): 456-475

[25] Willams AN, Li W, Wang K-H. Water wave interaction with a floating porous cylinder. Ocean Engng., 2000, 27: 1-28

[26] Yu X. Diffraction of water waves by porous breakwaters. J. Waterway, Port, Coastal, Ocean Engng., 1995, 121: 275282

[27] Zhao F, Kinoshita T, Bao W, Wan R, Liang Z, Huang L. Hydrodynamics identities and wave-drift force of a porous body. Appl. Ocean Res., 2011, 33: 169-177

[28] Zhao F, Bao W, Kinoshita T, Itakura H. Theoretical and experimental study of a porous cylinder floating in waves. J. Offsh. Mech. Arctc. Engng., 2011, 133: 011301-1–10