Nature of Wave Modes in a Coupled Viscoelastic Layer over Water
Publication: Journal of Engineering Mechanics
Volume 143, Issue 10
Abstract
A theoretical study of wave modes in a system of layered materials is presented. The system consists of a floating linear viscoelastic layer over inviscid water. The viscoelastic cover is assumed to obey the Voigt constitutive law. As in many other layered systems, multiple wave modes are discovered. Guided by the roots under pure elastic and pure viscous conditions, the nature of all roots in the dispersion relation is identified for the viscoelastic case. Wave modes include the evanescent, gravity, shear, pressure, interfacial, and Rayleigh-Lamb. All of these previously known waves in elastic solid or fluid over fluid systems are found in the present system of a viscoelastic material floating over water. An analytic criterion for the presence of mode swap in cases with low viscosity is obtained, and the origin of this mode swap phenomenon is discussed. In the vicinity of mode swap, both wave modes are important. Away from this region, the gravity wave mode dominates the free-surface motion.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors thank the anonymous reviewers for their very helpful suggestions. This work is supported in part by the Office of Naval Research, Grant No. N00014-13-1-0294, Ministry of Education, Singapore, through AcRF Tier-2 Grant No. MOE2013-T2-1-054, with in-kind support from the Office of Naval Research Global Grant No. N62909-15-1-2069. This study was conducted when the first author was a postdoctoral fellow at Clarkson University.
References
Aki, K., and Richards, P. G. (2009). Quantitative seismology, 2nd Ed., Univ. Science Books, Sausalito, CA.
Craik, A. D. D. (1985). Wave interactions and fluid flows, Cambridge University Press, Cambridge, U.K., 322.
Dalrymple, R., Losada, M., and Martin, P. (1991). “Reflection and transmission from porous structures under oblique wave attack.” J. Fluid Mech., 224, 625–644.
Dalrymple, R. A., and Liu, P. L. (1978). “Waves over soft muds: A two-layer fluid model.” J. Physical Oceanography, 8(6), 1121–1131.
Doble, M. J., De Carolis, G., Meylan, M. H., Bidlot, J.-R., and Wadhams, P. (2015). “Relating wave attenuation to pancake ice thickness, using field measurements and model results.” Geophys. Res. Lett., 42(11), 4473–4481.
Fox, C., and Squire, V. A. (1990). “Reflection and transmission characteristics at the edge of shore fast sea ice.” J. Geophys. Res.: Oceans, 95(C7), 11629–11639.
Graff, K. F. (1975). Wave motion in elastic solids, Ohio State University Press, Columbus, OH, 649.
Greenhill, A. G. (1886). “Wave motion in hydrodynamics.” Am. J. Math., 9(1), 62–96.
Hill, D. F., and Foda, M. A. (1999). “Effects of viscosity and elasticity on the nonlinear resonance of internal waves.” J. Geophys. Res., 104(C5), 10951–10957.
Jain, M. (2007). “Wave attenuation and mud entrainment in shallow waters.” Ph.D. dissertation, Univ. of Florida, Gainesville, FL, 210.
Keller, J. B. (1998). “Gravity waves on ice-covered water.” J. Geophy. Res.: Oceans, 103(C4), 7663–7669.
Lamb, S. H. (1932). Hydrodynamics, Dover, New York, 768.
Maa, J., and Mehta, A. (1990). “Soft mud response to water waves.” J. Waterway Port Coastal Ocean Eng., 634–650.
Macpherson, H. (1980). “The attenuation of water waves over a non-rigid bed.” J. Fluid Mech., 97(4), 721–742.
MATLAB [Computer software]. Mathworks, Natick, MA.
Mei, C. C., Krotov, M., Huang, Z., and Huhe, A. (2010). “Short and long waves over a muddy seabed.” J. Fluid Mech., 643(1), 33–58.
Mei, C. C., and Liu, K.-F. (1987). “A Bingham-plastic model for a muddy seabed under long waves.” J. Geophys. Res.: Oceans, 92(C13), 14581–14594.
Meylan, M., Bennetts, L. G., and Kohout, A. L. (2014). “In situ measurements and analysis of ocean waves in the Antarctic marginal ice zone.” Geophys. Res. Lett., 41(14), 5046–5051.
Mosig, J. E. M., Montiel, F., and Squire, V. A. (2015). “Comparison of viscoelastic-type models for ocean wave attenuation in ice-covered seas.” J. Geophys. Res.: Oceans, 120(9), 6072–6090.
Peters, A. S. (1950). “The effect of a floating mat on water waves.” Commun. Pure Appl. Math., 3(4), 319–354.
Phillips, O. M. (1969). The dynamics of the upper ocean, Cambridge University Press, London, 261.
Squire, V. A. (2007). “Of ocean waves and sea-ice revisited.” Cold Reg. Sci. Technol., 49(2), 110–133.
Squire, V. A., and Allan, A. J. (1980). “Propagation of flexural gravity waves in sea ice.” Sea Ice Processes and Models, Proc. Arctic Ice Dynamics Joint Experiment, University of Washington Press, Seattle, 327–338.
Thompson D. O., and Chimenti D. E., eds. (2013). Review of progress in quantitative nondestructive evaluation, Vol. 17A/17B, Springer, Berlin, 2127.
Thomson, J., Ackley, S. F., Shen, H. H., and Rogers, W. E. (2017). “The balance of ice, waves, and winds in the Arctic autumn.” EOS Earth and Space Science News, Hoboken, NJ.
Wadhams, P. (1986). “The seasonal ice zone.” N. Untersteier, ed., The Geophysics of sea ice, Plenum, New York, 825–991.
Wadhams, P., Squire, V. A., Goodman, D. J., Cowan, A. M., and Moore, S. C. (1988). “The attenuation rates of ocean waves in the marginal ice zone.” J. Geophys. Res., 93(C6), 6799–6818.
Wang, C. M., Watanabe, E., and Utsunomiya, T. (2007). Very large floating structures, CRC Press, Boca Raton, FL, 256.
Wang, R., and Shen, H. H. (2010). “Gravity waves propagating into an ice-covered ocean: A viscoelastic model.” J. Geophys. Res.: Oceans, 115(C6), 1–12.
Wang, R., and Shen, H. H. (2011). “A continuum model for the linear wave propagation in ice-covered oceans: An approximate solution.” Ocean Modell., 38(3), 244–250.
Weitz, M., and Keller, J. B. (1950). “Reflection of water waves from floating ice in water of finite depth.” Comm. Pure Appl. Math., 3(3), 305–318.
Yih, C.-S. (1980). Stratified flows, Academic Press, New York, 438.
Zhao, X., and Shen, H. H. (2013). “Ocean wave transmission and reflection between two connecting viscoelastic ice covers: An approximate solution.” Ocean Modell., 71, 102–113.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 143 • Issue 10 • October 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Sep 6, 2016
Accepted: Apr 11, 2017
Published online: Jul 19, 2017
Published in print: Oct 1, 2017
Discussion open until: Dec 19, 2017
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.