Skip to main content Accessibility help
×
Home

The interaction between a solitary wave and a submerged semicircular cylinder

  • M. J. Cooker (a1), D. H. Peregrine (a1), C. Vidal (a2) and J. W. Dold (a1)

Abstract

Numerical solutions for fully nonlinear two-dimensional irrotational free-surface flows form the basis of this study. They are complemented and supported by a limited number of experimental measurements. A solitary wave propagates along a channel which has a bed containing a cylindrical bump of semicircular cross-section, placed parallel to the incident wave crest. The interaction between wave and cylinder takes a variety of forms, depending on the wave height and cylinder radius, measured relative to the depth. Almost all the resulting wave motions differ from the behaviour which was anticipated when the study began. In particular, in those cases where the wave breaks, the breaking occurs beyond the top of the cylinder. The same wave may break in two different directions: forwards as usual, and backwards towards the back of the cylinder. In addition small reflected waves come from the region of uniform depth beyond the cylinder. Experimental results are reported which confirm some of the predictions made. The results found for solitary waves are contrasted with the behaviour of a group of periodic waves.

Copyright

References

Hide All
Dold, J. W. 1990 An efficient surface-integral algorithm for unsteady water waves. In preparation.
Dold, J. W. & Peregrine, D. H. 1986 An efficient boundary-integral method for steep unsteady water waves. In Methods for Fluid Dynamics II (ed. K. W. Morton & M. J. Baines), pp. 671679. Oxford University Press.
Evans, D. V. & Linton, C. M. 1989 Active devices for the reduction of wave intensity. Appl. Ocean Res. 11, 2932.
Forbes, L. K. & Schwartz, L. W. 1982 Free-surface flow over a semi-circular obstruction. J. Fluid Mech. 114, 299314.
New, A. L. 1983 On the breaking of water waves. Ph.D. thesis, University of Bristol, UK.
New, A. L. & Dyer, K. R. 1988 Internal waves and mixing in stratified estuarine flows. In Physical Processes in Estuaries (ed. J. Dronkers & W. van Leussen), pp. 239254. Springer.
New, A. L., Dyer, K. R. & Lewis, R. E. 1986 Predictions of the generation and propagation of internal waves and mixing in a partially stratified estuary. Estuar. Coast. Shelf Sci. 22, 199214.
New, A. L., Dyer, K. R. & Lewis, R. E. 1987 Internal waves and intense mixing periods in a partially stratified estuary. Estuarine Coastal Shelf Sci. 24, 1533.
Peregrine, D. H. 1990 The surface of steep unsteady water waves. In Mathematics and Computation of Deforming Surfaces (ed. J. C. R. Hunt). Oxford University Press (to appear).
Seabra-Santos, F. J., Renouard, D. P. & Temperville, A. M. 1987 Numerical and experimental study of the transformation of a solitary wave over a shelf or isolated obstacle. J. Fluid Mech. 176, 117134.
Tanaka, M. 1986 The stability of solitary waves. Phys. Fluids 29, 650655.
Tanaka, M., Dold, J. W., Lewy, M. & Peregrine, D. H. 1987 Instability and breaking of a solitary wave. J. Fluid Mech. 185, 235248.
Teles da Silva, A. F. 1989 Applications of boundary-integral methods to the study of steep free-surface waves, Ph.D. thesis, University of Bristol, UK.
Vinje, T. & Brevig, P. 1981 Nonlinear ship motions. 3rd Intl Conf. on Numerical Ship Hydrodynamics, Paris, France.
Yasuda, T., Hara, M. & Tanaka, M. 1990 A computational model of the deformation including overturning of a solitary wave over a submerged obstacle. Wave Motion (submitted).
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed