Capillary-gravity waves against a corrugated vertical cliff
- 20 Downloads
An analysis involving a transformation of the velocity potential and a Fourier Sine Transform technique is described to study the effect of surface tension on incoming surface waves against a vertical cliff with a periodic wall perturbation. Known results are recovered as particular cases of the general problem considered. An analytical expression is derived for the surface elevation, at far distances from the shore-line, by using Watson's lemma and a representative table of numerical values of the coefficients of the resulting asymptotic expansion is also presented.
KeywordsFourier Surface Tension Sine Surface Wave Asymptotic Expansion
Unable to display preview. Download preview PDF.
- 1.Chakrabarti, A. and Nalini, V.N.: Hydrodynamic pressure on a dam with a periodically corrugated reservoir bed. Acta Mechanica 60 (1986) 91–97.Google Scholar
- 2.Erdogan, F.: Stress distribution in bonded dissimilar materials with cracks. J. Appl. Mech. 32 (1965) 403–410.Google Scholar
- 3.Faulkner, T.R.: The diffraction of an obliquety incident surface wave by a vertical barrier of finite depth. Proc. Cambridge Philos. Soc. 62 (1966) 829–838.Google Scholar
- 4.Packham, B.A.: Capillary-gravity waves against a vertical cliff. Proc. Cambridge Philos. Soc. 64 (1968) 827–832.Google Scholar
- 5.Rhodes Robinson: On the forced surface wave due to a vertical wave-maker in the presence of surface tension. Proc. Cambridge Philos. Soc. 70 (1971) 323–337.Google Scholar
- 6.Sneddon, I.N.: The Use of Integral Transforms. Tata McGraw-Hill, New Delhi (1974).Google Scholar
- 7.Stoker, J.J.: Surface waves in water of variable depth, Quartly. of Appl. Math. 5 (1947) 1–54.Google Scholar
- 8.Williams, W.E.: Note on the scattering of water waves by a vertical barrier. Proc. Cambridge Philos. Soc. 62 (1966) 507–509.Google Scholar
- 9.Williams, W.E.: Partial Differential Equations. Clarendon, Oxford (1980) p. 232.Google Scholar