Hostname: page-component-84b7d79bbc-x5cpj Total loading time: 0 Render date: 2024-07-27T16:57:35.995Z Has data issue: false hasContentIssue false
  • English
  • Français

Wave motion in a viscous fluid of variable depth Part 2. Moving contact line

Published online by Cambridge University Press:  26 April 2006

John Miles
John Miles
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, San Diego, La Jolla, CA 92093-0225, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

An earlier derivation (Miles 1990a) of the partial differential equation for the complex amplitude of a gravity–capillary wave in a shallow, viscous liquid of variable depth and fixed contact line is extended to accommodate a meniscus with a moving contact line at which the slope of the meniscus is assumed to be proportional to (but not necessarily in phase with) the velocity. The motion of the contact line implies capillary dissipation, which is absent for a fixed contact line. The results are applied to the normal reflection of a wave incident from a region of uniform depth on a beach of uniform slope. The reflection coefficient has the form R = R1RνRc, where R1 is the coefficient for an ideal fluid, and Rν and Rc comprise the respective effects of viscosity and capillarity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 223 , February 1991 , pp. 47 - 55
Copyright
© 1991 Cambridge University Press

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

Ablett, R.: 1923 An investigation of the angle of contact between paraffin wax and water. Phil. Mag. 46, 244–256.Google Scholar
Dussan, V. E. B.: 1979 On the spreading of liquids on solid surfaces: static and dynamic contact lines. Ann. Rev. Fluid Mech. 11, 371–400.Google Scholar
Hocking, L. M.: 1987 The damping of capillary-gravity waves at a rigid boundary. J. Fluid Mech. 179, 253–266.Google Scholar
Ince, E. L.: 1944 Ordinary Differential Equations. Dover.
Lamb, H.: 1928 Statics. Cambridge University Press.
Lamb, H.: 1932 Hydrodynamics. Cambridge University Press.
Lighthill, M. J.: 1957 The fundamental solution for small steady three-dimensional disturbances to a two-dimensional parallel shear flow. J. Fluid Mech. 3, 113–144.Google Scholar
Mahony, J. J. & Pritchard, W. G., 1980 Wave reflexion from beaches. J. Fluid Mech. 101, 809–832.Google Scholar
Miles, J. W.: 1967 Surface-wave damping in closed basins. Proc. R. Soc. Lond. A 297, 459–475.Google Scholar
Miles, J.: 1990a Wave motion in a viscous fluid of variable depth. J. Fluid Mech. 212, 365–372 (referred to herein as I).Google Scholar
Miles, J.: 1990b Wave reflection from a gently sloping beach. J. Fluid Mech. 214, 59–66.Google Scholar
Miles, J.: 1990c A note on surface films and surface waves. Wave Motion (in press).Google Scholar