Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-27T08:48:00.922Z Has data issue: false hasContentIssue false
  • English
  • Français

Instability of unsteady flows or configurations Part 1. Instability of a horizontal liquid layer on an oscillating plane

Published online by Cambridge University Press:  28 March 2006

Chia-Shun Yih
Chia-Shun Yih
Affiliation:
Department of Engineering Mechanics, The University of Michigan
Get access Rights & Permissions [Opens in a new window]

Abstract

A layer of viscous liquid with a free surface is set in motion by the lower boundary moving simple-harmonically in its own plane. The stability of this motion is investigated. Since the primary flow is time-dependent, the time variable cannot be separated from at least one space variable, and a new approach must be used to investigate the problem. In this paper the stability of long waves is studied by a perturbation method which has not been applied before to problems of stability of unsteady flows, and it is found that the flow under consideration can be unstable for long waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 31 , Issue 4 , 18 March 1968 , pp. 737 - 751
Copyright
© 1968 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

Benjamin, T. B. 1957 Wave formation in laminar flow down an inclined plane J. Fluid Mech. 2, 554–75.Google Scholar
Benjamin, T. B. & Ursell, F. 1954 The stability of the plane free surface of a liquid in vertical periodic motion. Proc. Roy. Soc. Lond A 225, 505–15.Google Scholar
Coddington, E. A. & Levinson, N. 1955 Theory of Ordinary Differential Equations. New York: McGraw-Hill.
Conrad, P. W. & Criminale, W. O. 1965 The stability of time-dependent laminar flow: parallel flows. ZAMP 16, 233.Google Scholar
Currie, I. G. 1967 The effect of heating rate on stability of stationary fluids J. Fluid. Mech. 29, 337–48.Google Scholar
Ince, E. L. 1944 Ordinary Differential Equations. New York: Dover.
Joseph, D. D. 1966 Nonlinear stability of the Boussinesq equations J. Rat. Mech. Analy. 22, 163–84.Google Scholar
Orr, W. MCF. 1907 The stability or instability of the steady motions of a perfect liquid and of a viscous liquid. Part II: a viscous liquid. Proc. Roy. Irish Acad. 27, 69–138.Google Scholar
Squire, H. B. 1933 On the stability for three-dimensional disturbances of viscous fluid flow between parallel walls. Proc. Roy. Soc. Lond. A 142, 621–8.Google Scholar
Yih, C.-S. 1963 Stability of liquid flow down an inclined plane Phys. Fluids, 6, 321–34.Google Scholar
Yih, C.-S. 1966 Instability due to viscosity stratification J. Fluid Mech. 27, 337–352.Google Scholar