Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-01T20:09:42.585Z Has data issue: false hasContentIssue false
  • English
  • Français

Contact line dynamics and boundary layer flow during reflection of a solitary wave

Published online by Cambridge University Press:  13 July 2012

Yong Sung Park ,
Philip L.-F. Liu  and
I-Chi Chan
Yong Sung Park*
Affiliation:
Division of Civil Engineering, University of Dundee, Dundee DD1 4HN, UK
Philip L.-F. Liu
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA Institute of Hydrological and Oceanic Sciences, National Central University, Jhongli, Taoyuan 320, Taiwan
I-Chi Chan
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
*
†Email address for correspondence: y.s.park@dundee.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we present a set of wave flume experiments for a solitary wave reflecting off a vertical wall. A particle tracking velocimetry (PTV) technique is used to measure free-surface velocity and the velocity field in the vicinity of the moving contact line. We observe that the free surface undergoes the so-called rolling motion as the contact line moves up and down the vertical wall, and fluid particles on the free surface almost always flow toward the wall except at the end of the reflection process. As the contact line descends along the wall, wall boundary layer flows move in a downward direction and therefore the boundary layer acts like a conduit through which the surface-rolling-induced flow escapes from the meniscus. However, during the last phase of the reflection process flow reversal occurs inside the wall boundary layer. An approximate analytical solution is developed to explain the flow reversal feature. Very good agreement between the approximate theory and measured data is obtained. Because of the flow reversal, boundary layer flows collide with the surface-rolling-induced flows. The collision gives rise to a jet ejecting from the meniscus into the water body, which later evolves into a small eddy. It is noticed that the fluid particles in different regions such as the free stream, the free-surface boundary layer and the wall boundary layer, can be transported to other regions by passing through the meniscus.

JFM classification

Boundary Layers: Boundary layer structure Interfacial Flows (free surface): Contact lines Waves/Free-surface Flows: Solitary waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 707 , 25 September 2012 , pp. 307 - 330
Copyright
Copyright © Cambridge University Press 2012

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

1. Butkovsky, A. G. 1982 Green’s Functions and Transfer Functions Handbook. Halsted Press/Wiley.Google Scholar
2. Byatt-Smith, J. G. B. 1988 The reflection of a solitary wave by a vertical wall. J. Fluid Mech. 197, 503–521.CrossRefGoogle Scholar
3. Byatt-Smith, J. G. B. 1989 The head-on interaction of two solitary waves of unequal amplitude. J. Fluid Mech. 205, 573–579.CrossRefGoogle Scholar
4. Chan, R. K.-C. & Street, R. L. 1970 A computer study of finite-amplitude water waves. J. Comput. Phys. 6, 68–94.CrossRefGoogle Scholar
5. Cooker, M. J., Weidman, P. D. & Bale, D. S. 1997 Reflection of a high-amplitude solitary wave at a vertical wall. J. Fluid Mech. 342, 141–158.CrossRefGoogle Scholar
6. Cox, R. G. 1998 Inertial and viscous effects on dynamic contact angles. J. Fluid Mech. 357, 249–278.CrossRefGoogle Scholar
7. Craig, W., Guyenne, P., Hammack, J., Henderson, D. & Sulem, C. 2006 Solitary wave interactions. Phys. Fluids 18, 057106.CrossRefGoogle Scholar
8. Dalziel, S. B. 2008 Digiflow user guide. http://www.dalzielresearch.com/digiflow/.Google Scholar
9. Dussan V, E. B. 1979 On the spreading of liquids on solid surfaces: static and dynamic contact lines. Annu. Rev. Fluid Mech. 11, 371–400.CrossRefGoogle Scholar
10. Dussan V, E. B. & Davis, S. H. 1974 On the motion of a fluid–fluid interface along a solid surface. J. Fluid Mech. 65, 71–95.CrossRefGoogle Scholar
11. Eggers, J. & Stone, H. A. 2004 Characteristic lengths at moving contact lines for a perfectly wetting fluid: the influence of speed on the dynamic contact angle. J. Fluid Mech. 505, 309–321.CrossRefGoogle Scholar
12. Goring, D. K. 1979 Tsunamis: the propagation of long waves onto a shelf. PhD dissertation, California Institute of Technology.Google Scholar
13. Grimshaw, R. 1971 The solitary wave in water of variable depth. Part 2. J. Fluid Mech. 46, 611–622.CrossRefGoogle Scholar
14. Hocking, L. M. 1987a The damping of capillary–gravity waves at a rigid boundary. J. Fluid Mech. 179, 253–266.CrossRefGoogle Scholar
15. Hocking, L. M. 1987b Waves produced by a vertically oscillating plate. J. Fluid Mech. 179, 267–281.CrossRefGoogle Scholar
16. Hocking, L. M. 1987c Reflection of capillary–gravity waves. Wave Motion 9, 217–226.CrossRefGoogle Scholar
17. Hocking, L. M. & Davis, S. H. 2002 Inertial effects in time-dependent motion of thin films and drops. J. Fluid Mech. 467, 1–17.CrossRefGoogle Scholar
18. Liu, P. L.-F., Park, Y. S. & Cowen, E. A. 2007 Boundary layer flow and bed shear stress under a solitary wave. J. Fluid Mech. 574, 449–463.CrossRefGoogle Scholar
19. Liu, P. L.-F., Simarro, G., Vandever, J. & Orfila, A. 2006 Experimental and numerical investigation of viscous effects on solitary wave propagation in a wave tank. Coast. Engng 53, 181–190.CrossRefGoogle Scholar
20. Maxworthy, T. 1976 Experiments on collisions between solitary waves. J. Fluid Mech. 76, 177–185.CrossRefGoogle Scholar
21. McHugh, J. P. & Watt, D. W. 1998 Surface waves impinging on a vertical wall. Phys. Fluids 10, 324–326.CrossRefGoogle Scholar
22. Mei, C. C. & Liu, P. L.-F. 1973 The damping of surface gravity waves in a bounded liquid. J. Fluid Mech. 59, 239–256.CrossRefGoogle Scholar
23. Miles, J. 1990 Capillary-viscous forcing of surface waves. J. Fluid Mech. 219, 635–646.CrossRefGoogle Scholar
24. Ngan, C. G. & Dussan, V. E. B. 1982 On the nature of the dynamic contact angle: an experimental study. J. Fluid Mech. 118, 27–40.CrossRefGoogle Scholar
25. Su, C. H. & Mirie, R. M. 1980 On head-on collisions between two solitary waves. J. Fluid Mech. 98, 509–525.CrossRefGoogle Scholar
26. Tanaka, M. 1986 The stability of solitary waves. Phys. Fluids 29, 650–655.CrossRefGoogle Scholar
27. Ting, C.-L. & Perlin, M. 1995 Boundary conditions in the vicinity of the contact line at a vertically oscillating upright plate: an experimental investigation. J. Fluid Mech. 295, 263–300.CrossRefGoogle Scholar
28. Zarruk, G. A 2005 Measurement of free surface deformation in PIV images. Meas. Sci. Technol. 16, 1970–1975.CrossRefGoogle Scholar

Park et al. supplementary movie

The movie shows the formation of the jet as well as the induced clockwise eddy during the last phase of the solitary wave reflection. Note that we only include every fifth frame in the movie to reduce the file size, and it is ten times slower than the real time. At the frame in which the jet is formed, the red half-circle in the movie indicates the locations of the jet.

Download Park et al. supplementary movie(Video)
Video 872.5 KB

Park et al. supplementary movie

The movie shows the formation of the jet as well as the induced clockwise eddy during the last phase of the solitary wave reflection. Note that we only include every fifth frame in the movie to reduce the file size, and it is ten times slower than the real time. At the frame in which the jet is formed, the red half-circle in the movie indicates the locations of the jet.

Download Park et al. supplementary movie(Video)
Video 2.9 MB