Scattering of flexural waves by multiple narrow cracks in ice sheets floating on water. (English) Zbl 1231.86006
Summary: An explicit solution is derived for the reflection and transmission of flexural-gravity waves propagating on a uniform elastic ice sheet floating on water which are obliquely incident upon any number, \(N\), of narrow parallel cracks of arbitrary separation. The solution is expressed in terms of a system of \(2N\) linear equations for the jumps in the displacements and gradients across each of the cracks. A number of interesting features of the problem are addressed including the scattering by periodically spaced arrays of cracks, and examples of non-uniqueness, or trapped waves, in the case of four cracks. The problem of wave reflection by a semi-infinite periodic array of cracks is also formulated exactly in terms of a convergent infinite system of equations and relies on certain properties of the so-called Bloch problem for wave propagation through infinite periodic array of cracks.
MSC:
| 86A05 | Hydrology, hydrography, oceanography |
| 74J05 | Linear waves in solid mechanics |
| 74J20 | Wave scattering in solid mechanics |
References:
| [1] | Evans, D. V.; Porter, R., Wave scattering by narrow cracks in ice sheets floating on water of finite depth, J. Fluid Mech., 484, 143-165 (2003) · Zbl 1031.76009 |
| [2] | Squire, V. A.; Dugan, J. P.; Wadhams, P.; Rottier, P. J.; Liu, A. K., Of ocean waves and ice sheets, Ann. Rev. Fluid Mech., 27, 115-168 (1995) |
| [3] | Squire, V. A.; Dixon, A. W., How a region of cracked sea ice affects ice-coupled wave propagation, Ann. Glaciol., 33, 327-332 (2001) |
| [4] | Leppington, F. G., Acoustic scattering by membranes and plates with line constraints, J. Sound Vib., 58, 3, 319-332 (1978) · Zbl 0377.76072 |
| [5] | J.B. Lawrie, D. Abrahams, On the propagation and scattering of fluid-structural waves in a three-dimensional duct bounded by thin elastic walls, in: Proc. IUTAM Symp. Manchester, UK. Kluwer Academic Publishers, 2002, pp. 279-288.; J.B. Lawrie, D. Abrahams, On the propagation and scattering of fluid-structural waves in a three-dimensional duct bounded by thin elastic walls, in: Proc. IUTAM Symp. Manchester, UK. Kluwer Academic Publishers, 2002, pp. 279-288. · Zbl 1183.76858 |
| [6] | Ashcroft, N. W.; Mermin, N. D., Solid State Physics (1976), W.B. Saunders: W.B. Saunders Philadelphia · Zbl 1118.82001 |
| [7] | Chou, T., Band structure of surface flexural-gravity waves along periodic interfaces, J. Fluid Mech., 369, 333-350 (1998) · Zbl 0928.76019 |
| [8] | Nishimoto, M.; Ikuno, H., Analysis of electromagnetic wave diffraction by a semi-infinite strip grating and evaluation of end-effects, Prog. Electromagn. Res., 23, 39-58 (1999) |
| [9] | Newman, J. N., Propagation of water waves past long two-dimensional obstacles, J. Fluid Mech., 23, 23-29 (1965) · Zbl 0136.46602 |
| [10] | Kriegsmann, G. A., Scattering matrix analysis of a photonic Fabry-Perot resonator, Wave Motion, 37, 43-61 (2003) · Zbl 1163.74388 |
| [11] | Kyriazidou, C. A.; Contopangos, H. F.; Merill, W. M.; Alexopoulos, N. G., Artificial versus natural crystals: effective wave impedance of printed photonic bandgap materials, IEEE Trans. Antennas Propagat., 48, 95-105 (2000) · Zbl 0955.78012 |
| [12] | Chamberlain, P. G.; Porter, D., Decomposition methods for wave scattering by topography with application to ripple beds, Wave Mot., 22, 201-214 (1995) · Zbl 0968.76520 |
| [13] | Botten, L. C.; Nicorovici, N. A.; McPhedran, R. C.; Martin de Sterke, C.; Asatryan, A. A., Photonic band structure calculations using scattering matrices, Phys. Rev. E, 64, 046603 (2001) |
| [14] | Porter, R.; Porter, D., Scattered and free waves over periodic beds, J. Fluid Mech., 483, 129-163 (2003) · Zbl 1055.76005 |
| [15] | Fox, C.; Squire, V. A., On the oblique reflexion and transmission of ocean waves from the shore fast sea ice, Phil. Trans. R. Soc. A, 347, 1682, 185-218 (1994) · Zbl 0816.73009 |
| [16] | McIver, P., Scattering of water waves by two surface-piercing barriers, IMA J. Appl. Math., 35, 1-17 (1985) · Zbl 0591.76022 |
| [17] | Porter, R.; Evans, D. V., Complementary approximations to wave scattering by vertical barriers, J. Fluid Mech., 294, 155-180 (1995) · Zbl 0842.76007 |
| [18] | Linton, C. M.; Kuznetsov, N. G., Non-uniqueness in two-dimensional water wave problems: numerical evidence and geometrical restrictions, Proc. R. Soc. Lond. A, 453, 2437-2460 (1997) · Zbl 1067.76530 |
| [19] | Porter, R., Trapping of water waves by pairs of submerged cylinders, Proc. R. Soc. Lond. A, 458, 607-624 (2002) · Zbl 1001.76016 |
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