Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-19T05:49:48.241Z Has data issue: false hasContentIssue false
  • English
  • Français

Taylor instability of a non-uniform free-surface flow

Published online by Cambridge University Press:  29 March 2006

G. Dagan
G. Dagan
Affiliation:
Israel Institute of Technology, Haifa, Israel
Get access Rights & Permissions [Opens in a new window]

Abstract

The evolution of a small disturbance in a three-dimensional steady free-surface flow is investigated. The radius of curvature of the free surface and the length scale characterizing the non-uniformity of the velocity are assumed to be of the same order of magnitude. It is shown that the local rate of growth of the amplitude of the disturbance depends on both the normal pressure gradient (as in the case of Taylor instability) and the rate of strain on the free surface. Application of the theory to rising gaseous bubbles and gravity water waves is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 67 , Issue 1 , 14 January 1975 , pp. 113 - 123
Copyright
© 1975 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

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Bellman, R. & Pennington, R. H. 1954 Effects of surface tension and viscosity on Taylor instability. Quart. AppZ. Math., 12, 151.Google Scholar
Dagan, G. & Tulin, M. P. 1972 Two-dimensional free-surface gravity flow past blunt bodies. J. Fluid Mech., 51, 529.Google Scholar
Longuet-Higgins, M. S. & Stewart, R. W. 1960 Changes in the form of short gravity waves on long waves and tidal currents. J. Fluid Mech., 8, 565.Google Scholar
Longuet-Higcins, M. S. & Stewart, R. W. 1961 The changes in amplitude of short gravity waves on steady non-uniform currents. J. Fluid Mech., 10, 529.Google Scholar
Rajappa, N. R. 1970 On the instability of fluid surfaces when accelerated perpendicular to their planes. Acta Meclmnica, 10, 193.Google Scholar
Rowe, P. N. & Partridge, B. A. 1964 A note on the initial motion and break-up of a two-dimensional air bubble in water. Chem. Engng Sci., 19, 81.Google Scholar
Schwartz, L. W. 1974 Computer extension and analytic continuation of Stokes’ expansion for gravity waves. J. Fluid Mech., 62, 553Google Scholar
Taylor, G. I. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their plane. Proc. Roy. Soc. A 201, 192.Google Scholar
Von Schwind, J. J. & Reid, R. O. 1972 Characteristics of gravity waves of permanent form. J. Geophys. Res., 77, 420.Google Scholar
Wehausen, J. V. & Laitone, E. V. 1960 Surface waves. In Encyclopaedia of Physics vol. 9, pp. 446–771. Springer.
Whitham, G. B. 1962 Mass, momentum and energy flux in water waves. J. Fluid Mech., 12, 135Google Scholar
Wu, T. Y. 1968 Inviscid cavity and wake flows. In Inviscid cavity and wake flows Basic Developments in Fluid Dynamics.