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Waves due to a steadily moving source on a floating ice plate. Part 2

Published online by Cambridge University Press:  21 April 2006

R. M. S. M. Schulkes ,
R. J. Hosking  and
A. D. Sneyd
R. M. S. M. Schulkes
Affiliation:
University of Waikato, Hamilton, New Zealand
R. J. Hosking
Affiliation:
University of Waikato, Hamilton, New Zealand
A. D. Sneyd
Affiliation:
University of Waikato, Hamilton, New Zealand
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Abstract

This paper extends previous theoretical work on waves in floating ice plates to take account of the following effects: (i) compressive stress in the plane of the plate, (ii) uniform flow in the underlying water, and (iii) stratification of the underlying water. The first two effects are unlikely to be important in practice, causing respectively a slight decrease in phase speed and mainly a re-orientation of the wave pattern due to a steadily moving source. A two-layer model is used to describe stratification, which introduces a new system of slow internal waves associated with the layer interface, while the surface flexural waves are only slightly modified. In the case of unstratified water there is a minimum speed cmin such that more slowly moving sources excite a static rather than a wavelike response in the ice. With stratified water there remains a variety of steady wave patterns due to the internal waves, at source speeds below cmin. Another important effect of stratification is to greatly increase wave drag. For certain source load distributions, internal-wave amplitudes may grow until linear theory is no longer applicable.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 180 , July 1987 , pp. 297 - 318
Copyright
© 1987 Cambridge University Press

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References

Bates, H. F. & Shapiro, L. H. 1980 Long period gravity waves in ice-covered sea. J. Geophys. Res. 85, 1095–1100.Google Scholar
Davys, J. W. 1984 Waves in floating ice plates. M.Sc. thesis, University of Waikato.
Davys, J. W., Hosking, R. J. & Sneyd, A. D. 1985 Waves due to a steadily moving source on a floating ice plate. J. Fluid Mech. 158, 269–287.Google Scholar
Garrett, C. & Munk, W. 1979 Internal waves in the ocean. Ann. Rev. Fluid Mech. 11, 339–369.Google Scholar
Greenhill, A. G. 1887 Wavemotion in hydrodynamics. Am. J. Math. 9, 62.Google Scholar
Kerr, A. D. 1979 The critical velocities of a floating ice plate subjected to in-plane forces and a moving load. U.S. Army CRREL Res. Rep. 79–19.Google Scholar
Kerr, A. D. 1983 The critical velocities of a moving load on a floating ice plate that is subjected to inplane forces. Cold Regions Sci. Tech. 6, 267–274.Google Scholar
Lamb, H. 1945 Hydrodynamics. Dover.
Landau, L. D. & Lifshitz, E. M. 1959 Theory of Elasticity. Pergamon.
Lewis, E. L. & Walker, E. R. 1970 The water structure under a growing ice sheet. J. Geophys. Res. 75, 6836–6845.Google Scholar
Lighthill, M. J. 1978 Waves in Fluids. Cambridge University Press.
Longuet-Higgins, M. S. 1977 Some effects of finite steepness on the generation of waves by wind. In A Voyage of Discovery: George Deacon 70th Anniversary Volume (ed. M. Angel), pp. 393–403. Pergamon
Seifert, W. F. & Langleben, M. P. 1972 Air drag coefficient and roughness length of a cover of sea ice. J. Geophys. Res. 77, 2708–2713.Google Scholar
Squire, V. A., Robinson, W. H., Haskell, T. G. & Moore, S. G. 1985 Dynamic strain response of lake and sea ice to moving loads. Cold Regions Sci. Tech., 11, 123–139.Google Scholar