Hostname: page-component-7dd5485656-k8lnt Total loading time: 0 Render date: 2025-10-31T01:14:24.462Z Has data issue: false hasContentIssue false
  • English
  • Français

Capillary–gravity Kelvin–Helmholtz waves close to resonance

Published online by Cambridge University Press:  26 April 2006

V. Bontozoglou  and
T. J. Hanratty
V. Bontozoglou
Affiliation:
Department of Chemical Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA Present address: Chemical Process Engineering Research Institute, PO Box 19517, 54006 Thessaloniki, Greece.
T. J. Hanratty
Affiliation:
Department of Chemical Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Capillary–gravity waves of permanent form at the interface between two unbounded fluids in relative motion are considered. The range of wavelengths for an internal resonance with the second harmonic and a period-doubling bifurcation are found to depend on the current speed. The Kelvin–Helmholtz instability of short waves becomes strongly subcritical near resonance. It is speculated that this instability is needed to trigger a period-doubling bifurcation. This notion is used to explain the development of waves at short fetch and the initiation of liquid slugs for gas–liquid flow in a horizontal pipe.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 217 , August 1990 , pp. 71 - 91
Copyright
© 1990 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.)

Article purchase

Temporarily unavailable

References

Andritsos, N., Williams, L. & Hanratty, T. J. 1989 Effect of liquid viscosity on stratified-slug transition in horizontal pipe flow. Intl J. Multiphase Flow 15, 877.Google Scholar
Bontozoglou, V. & Hanratty, T. J. 1988 Effects of finite depth and current velocity on large amplitude Kelvin—Helmholtz waves. J. Fluid Mech. 196, 187.Google Scholar
Chen, B. & Saffman, P. G. 1979 Steady gravity—capillary waves on deep water. I. Weakly nonlinear waves. Stud. Appl. Maths 60, 183.Google Scholar
Chen, B. & Saffman, P. G. 1980 Steady gravity—capillary waves on deep water. II. Numerical results for finite amplitude. Stud. Appl. Maths 62, 95.Google Scholar
Choi, I. 1977 Contributions a l’étude des mechanisms physiques de la generation des ondes de capillarité—gravité à une interface air—eau. Thèse, Université d'Aix Marseille.
Cohen, L. S. & Hanratty, T. J. 1965 Generation of waves in the concurrent flow of air and liquid. AIChE J. 11, 138.Google Scholar
Drazin, P. G. 1970 Kelvin—Helmholtz instability of finite amplitude. J. Fluid Mech. 42, 321.Google Scholar
Hanratty, T. J. 1983 Interfacial instabilities caused by air flow over a thin liquid layer. Waves on Fluid Interfaces. Academic.
Kawai, S. 1979 Generation of initial wavelets by instability of a coupled shear flow and their evolution to wind waves. J. Fluid Mech. 93, 661.Google Scholar
Kordyban, E. S. & Ranov, T. 1970 Mechanism of slug formation in horizontal two-phase flow. J. Basic Engng 92D (4), 857.Google Scholar
Lin, P. Y. & Hanratty, T. J. 1986 Prediction of the initiation of slugs with linear stability theory. Intl J. Multiphase Flow 12, 79.Google Scholar
Maslowe, S. A. & Kelly, R. E. 1970 Finite amplitude oscillations in a Kelvin—Helmholtz flow. Intl J. Non-Linear Mech. 5, 427.Google Scholar
Miles, J. W. 1957 On the generation of surface waves by shear flows. J. Fluid Mech. 3, 185.Google Scholar
Miles, J. W. 1959 On the generation of surface waves by shear flows. Part 3: Kelvin—Helmholtz instability. J. Fluid Mech. 6, 583.Google Scholar
Miles, J. W. 1986 Weakly nonlinear Kelvin—Helmholtz waves. J. Fluid Mech. 172, 513.Google Scholar
Nayfeh, A. H. & Saric, W. S. 1972 Nonlinear waves in Kelvin—Helmholtz flow. J. Fluid Mech. 55, 311.Google Scholar
Pierson, W. J. & Fife, P. 1961 Some nonlinear properties of long-crested periodic waves with lengths near 2.44 centimeters. J. Geophys. Res. 66, 163.Google Scholar
Pullin, D. I. & Grimshaw, R. H. J. 1983 Nonlinear interfacial progressive waves near a boundary in a Boussinesq fluid. Phys. Fluids 26(4), 897.Google Scholar
Ramamonjarisoa, A., Baldy, S. & Choi, I. 1978 Laboratory studies of wind-wave generation, amplification and evolution. In Turbulent Fluxes through the Sea Surface, Wave Dynamics and Prediction. Plenum.
Saffman, P. G. & Yuen, H. C. 1982 Finite-amplitude interfacial waves in the presence of a current. J. Fluid Mech. 123, 459.Google Scholar
Schwartz, L. W. & Vanden-Broeck, J.-M. 1979 Numerical solution of the exact equations for capillary—gravity waves. J. Fluid Mech. 95, 119.Google Scholar
Taitel, Y. & Dukler, A. E. 1976 A model for predicting flow regime transitions in horizontal and near horizontal gas—liquid flow. AIChE J. 22, 47.Google Scholar
Vanden-Broeck, J.-M. 1980 Numerical calculation of gravity—capillary interfacial waves of finite amplitude. Phys. Fluids 23(9), 1723.Google Scholar
Wallis, G. B. & Dobson, J. E. 1973 The onset of slugging in horizontal stratified air—water flow. Intl J. Multiphase Flow 1, 173.Google Scholar
Weissman, M. A. 1979 Nonlinear wave packets in the Kelvin—Helmholtz instability. Phil. Trans. R. Soc. Lond. A 290, 639.Google Scholar
Wilton, J. R. 1915 On ripples. Phil. Mag. 29, 688.Google Scholar