Hostname: page-component-7b7567c8c-2rsb6 Total loading time: 0 Render date: 2026-11-12T22:54:40.805Z Has data issue: false hasContentIssue false
  • English
  • Français

Wave-current interactions: an experimental and numerical study. Part 1. Linear waves

Published online by Cambridge University Press:  20 April 2006

G. P. Thomas
G. P. Thomas
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TWPresent address: Department of Mathematical Physics, University College, Cork, Eire.
Get accessRights & Permissions [Opens in a new window]

Abstract

The interaction between a regular wavetrain and an adverse current containing an arbitrary distribution of vorticity, in two dimensions, is studied using a linear theory. The model is used to predict the wavelength and the particle velocities under the waves and these are found to agree well with experimentally obtained data for a number of current profiles. Surprisingly accurate predictions, for the profiles considered, were also obtained from an irrotational wave–current model in which the constant current has a value equal to the depth-averaged mean of the measured current profile. The changes in the wave amplitude as the current magnitude increases are predicted using an irrotational slowly varying model with good agreement being found between theory and experiment.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 110 , September 1981, pp. 457 - 474
Copyright
© 1981 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.)

Article purchase

Temporarily unavailable

References

Bretherton, F. P. & Garrett, G. J. R. 1968 Wavetrains in inhomogeneous moving media. Proc. Roy. Soc. A 302, 529–554.Google Scholar
Brevik, I. & Aas, B. 1980 Flume experiments on waves and currents. Coastal Engng 3, 149–177.Google Scholar
Dalrymple, R. A. 1973 Water wave models and wave forces with shear currents. Coastal & Ocean. Engng Lab., Univ. of Florida. Tech. Rep. 20.Google Scholar
Dalrymple, R. A. 1977 A numerical model for periodic finite-amplitude waves on a rotational fluid. J. Comp. Phys. 24, 29–42.Google Scholar
Evans, J. T. 1955 Pneumatic and similar breakwaters. Proc. Roy. Soc. A 231, 457–466.Google Scholar
Fenton, J. D. 1973 Some results for surface gravity waves on shear flows. J. Inst. Math. Applic. 12, 1–20.Google Scholar
Hoften, J. D. A. Van & Karaki, S. 1976 Interaction of Waves and a Turbulent Current. Proc. 15th Coastal Engng Conf., vol. 1, pp. 404–422.
Hughes, B. A. & Stewart, R. W. 1961 Interaction between gravity waves and a shear flow. J. Fluid Mech. 10, 385–400.Google Scholar
Jonsson, I. G., Brink-Kjaer, O. & Thomas, G. P. 1978 Wave action and set-down for waves on a shear current. J. Fluid Mech. 87, 401–416.Google Scholar
Longuet-Higgins, M. S. & Stewart, R. W. 1961 Changes in amplitude of short gravity waves on steady non-uniform currents. J. Fluid Mech. 10, 529–549.Google Scholar
Peregrine, D. H. 1976 Interaction of water waves and currents. Adv. Appl. Math. 16, 9–117.Google Scholar
Sarpkaya, T. 1955 Oscillatory gravity waves in flowing water. Proc. A.S.C.E. Engng Mech. Div. 81, 815.1–815.33.Google Scholar
Sarpkaya, T. 1957 Oscillatory gravity waves in flowing water. Trans. A.S.C.E. 122, 564–586.Google Scholar
Shaw, T. L. & Hutchinson, R. S. 1978 Assessment of hydrodynamic facilities for research in marine technology. Report submitted to Marine Technology Directorate of U.K. Science Research Council.
Taylor, G. I. 1955 The action of a surface current used as a breakwater. Proc. Roy. Soc. A 231, 466–478.Google Scholar
Thomas, G. P. 1979a Water wave-current interactions: a review. In Mechanics of Wave-Induced Forces on Cylinders (ed. T. L. Shaw), pp. 179–203. Pitman.
Thomas, G. P. 1979b Wave-current interactions: an experimental and numerical study. In Mechanics of Wave-Induced Forces on Cylinders (ed. T. L. Shaw), pp. 260–271. Pitman.
Ursell, F., Dean, R. G. & Yu, Y. S. 1960 Forced small-amplitude water waves: a comparison of theory and experiment. J. Fluid Mech. 7, 33–52.Google Scholar
Whitham, G. B. 1974 Linear and Non-linear Waves. Wiley-Interscience.
Yu, Y.-Y. 1952 Breaking of waves by opposing currents. Trans. Am. Geophys. Union 33, 39–41.Google Scholar