Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T10:10:15.312Z Has data issue: false hasContentIssue false
  • English
  • Français

The effect of a semi-contaminated free surface on mass transport

Published online by Cambridge University Press:  24 October 2008

D. Porter  and
B. D. Dore
D. Porter
Affiliation:
Department of Mathematics, University of Reading
B. D. Dore
Affiliation:
Department of Mathematics, University of Reading
Get access Rights & Permissions [Opens in a new window]

Abstract

The mass transport velocity field is determined for surface waves which propagate from a region with a clean free surface into a region beneath an inextensible surface film. The waves are assumed to be incident normally on the edge of the film. Determination of this velocity field requires the investigation of a mixed boundary value problem for the bi-harmonic equation, the solution of which is obtained using the Wiener–Hopf technique. Streamlines for the mean motion of the fluid particles are thus obtained. It is found that considerable vertical displacement of fluid is possible due to the presence of the surface film.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 75 , Issue 2 , March 1974 , pp. 283 - 294
Copyright
Copyright © Cambridge Philosophical Society 1974

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

REFERENCES

(1)Dore, B. D. and Porter, D.The edge effect of a surface film on gravity waves. (To be published in J. Inst. Math. Applics.)Google Scholar
(2)Longuet-Higgins, M. S.Mass transport in water waves. Philos. Trans. Roy. Soc. London, Ser. A245 (1953), 535–581.Google Scholar
(3)Huang, N. E.Mass transport induced by wave motion. J. Mar. Res. 28 (1970), 35–50.Google Scholar
(4)Dore, B. D.A study of mass transport in boundary layers at oscillating free surfaces and interfaces. Proceedings of the IUTAM Symposium on Unsteady Boundary Layers, Laval University, Quebec (1971), 1535–1583.Google Scholar
(5)Graebel, W. P.Slow viscous shear flow past a plate in a channel. Phys. Fluids 8 (1965), 1929–1935.CrossRefGoogle Scholar
(6)Ürlüata, U. and Mei, C. C.Mass transport in water waves. J. Geophys. Res. 75 (1970), 7611–7618.CrossRefGoogle Scholar
(7)Bagnold, R. A.Sand movement by waves: some small-scale experiments with sand of very low density. J. Inst. Civil Engrs (London) 27 (1947), 447–469.CrossRefGoogle Scholar
(8)Phillips, O. M. Chapter 3 of The dynamics of the upper ocean, p. 41 (Cambridge University Press, 1966).Google Scholar
(9)Koiter, W. T.Approximate solution of Wiener–Hopf type integral equations with applications. Nederl. Akad. Wetensch. Proc. Ser. B57 (1954), 558–579.Google Scholar
(10)Buchwald, V. T. and Doran, H. E.Eigenfunctions of plane elastostatics. II. A mixed boundary value problem of the strip. Proc. Roy. Soc. London, Ser. A284 (1965), 69–82.Google Scholar
(11)Richardson, S.A ‘stick–slip’ problem related to the motion of a free jet at low Reynolds numbers. Proc. Cambridge Philos. Soc. 67 (1970), 477–489.CrossRefGoogle Scholar
(12)Russell, R. C. H. and Osorio, J. D. C.An experimental investigation of drift profiles in a closed channel. Proc. 6th Conf. on Coastal Eng., Miami, Council on Wave Res., Univ. of California (1957), 171–193.Google Scholar
(13)Kinsman, B. Chapter 10 of Wind waves, p. 509 (Prentice-Hall, Inc., 1965).Google Scholar
(14)Wiegel, B. L. Chapter 2 of Oceanographical engineering, p. 61 (Prentice-Hall, Inc., 1964).Google Scholar
(15)Levich, V. G. Chapter 7 of Physico-chemical hydrodynamics, p. 393 (Prentice-Hall, Inc., 1962).Google Scholar
(16)Dorrestein, R.General linearized theory of the effect of surface films on water ripples. I. Nederl. Akad. Wetensch. Proc. Ser. B54 (1951), 260–272.Google Scholar