Abstract
In this note the two-dimensional problem of incoming surface waves against an approximately vertical wall or cliff in water of infinite depth is examined, using velocity potential formulation and linearized boundary-value problem theory for time-harmonic motion. The cliff has arbitrary profile but for simplicity is taken to be vertical at the free surface. The approximate first-order solution is determined subject to a dynamical edge condition apposite to the presence of surface tension, and contains partially reflected outgoing waves. The solution is obtained by perturbation theory in a form involving known unperturbed and first-order correction potentials that is applicable also to water of finite constant depth. The motivation for the note is to point out a correction in principle to the results of a recent investigation for a specific profile, in which reflexion is ignored and another error made in obtaining a first-order solution by a method that is restricted to infinite depth.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Chakrabarti, A., Capillary-gravity waves against a corrugated vertical cliff.Appl. Sci. Research 45 (1988) 303–317.
Hocking, L.M., Waves produced by a vertically oscillating plate.J. Fluid Mech. 179 (1987) 267–281.
Packham, B.A., Capillary-gravity waves against a vertical cliff.Proc. Cambridge Philos. Soc. 64 (1968) 827–832.
Rhodes-Robinson, P.F., On the forced surface waves due to a vertical wave-maker in the presence of surface tension.Proc. Cambridge Philos. Soc. 70 (1971) 323–337.
Rhodes-Robinson, P.F., Note on the reflexion of water waves at a wall in the presence of surface tension.Math. Proc. Cambridge Philos. Soc. 92 (1982) 369–373.
Rhodes-Robinson, P.F., The effect of surface tension on the progressive waves due to incomplete vertical wave-makers in water of infinite depth.Proc. Roy. Soc. Ser. A 435 (1991) 293–319.
Williams, W.E., Note on the scattering of water waves by a vertical barrier.Proc. Cambridge Philos. Soc. 62 (1966) 507–509.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rhodes-Robinson, P.F. Note on the reflexion of water waves at a nearly vertical cliff in the presence of surface tension. Appl. Sci. Res. 51, 599–609 (1993). https://doi.org/10.1007/BF00868002
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00868002