Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-05-13T13:37:33.581Z Has data issue: false hasContentIssue false
  • English
  • Français

Waves due to a steadily moving source on a floating ice plate

Published online by Cambridge University Press:  20 April 2006

J. W. Davys ,
R. J. Hosking  and
A. D. Sneyd
J. W. Davys
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.
Get access Rights & Permissions [Opens in a new window]

Abstract

The propagation of flexural waves in floating ice plates is governed by two restoring forces – elastic bending of the plate, and the tendency of gravity to make the upper surface of the supporting water horizontal. This paper studies steady wave patterns generated by a steadily moving source on a water–ice system that is assumed to be homogeneous and of infinite horizontal extent, using asymptotic Fourier analysis to give a simple description of the wave pattern far from the source. Short-wavelength elastic waves propagate ahead, while the long gravity waves appear behind; and, depending on the system parameters, one, two or no caustics may appear. Wavecrest patterns are shown, and the amplitude variation with direction from the source is given. Where the two caustics just merge together, a special mathematical function analogous to the Airy function is introduced to describe wave amplitudes. These waves can be detected by a strainmeter embedded in the ice, and we compare its theoretical response with some experimental measurements.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 158 , September 1985 , pp. 269 - 287
Copyright
© 1985 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bakhoom N. G. 1933 Asymptotic expansions of the function Fk(x) = Proc. Lond. Math. Soc. (2) 35, 83.Google Scholar
Bates, H. F. & Shapiro L. H. 1980 Long-period gravity waves in ice-covered sea. J. Geophys. Res. 85 (C2), 1095.Google Scholar
Bates, H. F. & Shapiro L. H. 1981 Stress amplification under a moving load on floating ice. J. Geophys. Res. 86 (C7), 6638.Google Scholar
Davys J. W. 1984 Waves in floating ice plates. M.Sc. thesis, University of Waikato.
Funnell R. H. 1982 Waves in sea ice. M.Sc. thesis, University of Waikato.
Greenhill A. G. 1887 Wave motion in hydrodynamics. Am. J. Maths 9, 62.Google Scholar
Kerr A. D. 1976 The bearing capacity of floating ice plates subjected to static or quasistatic loads. J. Glaciol. 17, 229.Google Scholar
Kerr A. D. 1983 The critical velocities of a load moving on a floating ice plate that is subjected to inplane forces. Cold Regions Sci. Tech. 6, 267.Google Scholar
Kheisin D. Ye. 1971 Some non-stationary problems of dynamics of the ice cover. In Studies in Ice Physics and Ice Engineering (ed. Iakolev). Israel Program for Scientific translations.
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). Pergamon.
Mills D. A. 1972 Waves in a sea ice cover. Horace Lamb Centre for Oceanog. Res., Flinders Univ. S. Australia, Res. Rep. 53.Google Scholar
Nevel D. E. 1970 Moving loads on a floating ice sheet. US Army CRREL Res. Rep. 261.Google Scholar
Squire, V. A. & Allan A. J. 1980 Propagation of flexural gravity waves in sea ice. In Sea Ice Processes and Models (ed. R. S. Pritchard). University of Washington Press.
Squire V. A., Robinson W. H., Haskell, T. G. & Moore S. C. 1985 Dynamic strain response of lake and sea ice to moving loads. Cold Regions Sci. Tech. (to appear).Google Scholar
Ursell F. 1970 Integrals with a large parameter. Paths of descent and conformal mappings. Proc. Camb. Phil. Soc. 67, 371.Google Scholar