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Large-amplitude interfacial waves on a linear shear flow in the presence of a current

Published online by Cambridge University Press:  26 April 2006

George Breyiannis ,
Vasilis Bontozoglou ,
Dimitris Valougeorgis  and
Apostolos Goulas
George Breyiannis
Affiliation:
Laboratory of Fluid Mechanics and Turbomachinery, Department of Mechanical Engineering, Aristotle University of Thessaloniki, 54006 Thessaloniki, Greece
Vasilis Bontozoglou
Affiliation:
Department of Mechanical Engineering, University of Thessaly, Pedion Areos, 38334 Volos, Greece
Dimitris Valougeorgis
Affiliation:
Laboratory of Fluid Mechanics and Turbomachinery, Department of Mechanical Engineering, Aristotle University of Thessaloniki, 54006 Thessaloniki, Greece
Apostolos Goulas
Affiliation:
Laboratory of Fluid Mechanics and Turbomachinery, Department of Mechanical Engineering, Aristotle University of Thessaloniki, 54006 Thessaloniki, Greece
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Abstract

The properties of two-dimensional steady periodic interfacial gravity waves between two fluids in relative motion and of constant vorticities and finite depths are investigated analytically and numerically. Particular attention is given to the effect of uniform vorticity, in the presence of a current velocity, on the two factors (identified in the literature as dynamical and geometrical limits) which limit the existence of steady gravity wave Solutions. The dynamical limit to the existence of steady Solutions is found to be significantly influenced by the uniform vorticity of the lower fluid. In particular, the effect of non-zero vorticity is qualitatively different between a very shallow and a relatively deep lower fluid. Profiles and flow fields corresponding to very steep waves are calculated for a wide range of parameter values. The effect of uniform vorticity on the interfacial wave structure is demonstrated through a direct comparison with irrotational waves. For negative vorticity and high current velocity, a new flow structure is found, consisting of a closed eddy attached to the interface below the crest. Resemblance with shallow water waves breaking under strong air flow, (described in the experimental literature as roll waves) is noted.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 249 , April 1993 , pp. 499 - 519
Copyright
© 1993 Cambridge University Press

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References

Andreussi, P., Asali, J. C. & Hanratty, T. J. 1985 Initiation of roll waves in gas–liquid flows. AIChE J. 31, 119.Google Scholar
Banner, M. L. & Phillips, O. M. 1974 On the incipient breaking of small scale waves. J. Fluid Mech. 65, 647.Google Scholar
Bateman, H. 1944 Partial Differential Equations. Cambridge University Press.
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
Drazin, P. G. 1970 Kelvin-Helmholtz instability of finite amplitude. J. Fluid Mech. 42, 321.Google Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Grimshaw, R. H. J. & Pullin, D. I. 1986 Extreme interfacial waves. Phys. Fluids 29, 2802.Google Scholar
Hanratty, T. J. 1983 Interfacial instabilities caused by the air flow over a thin liquid layer. In Waves on Fluid Interfaces(ed.R. E. Meyer), p. 221. Academic.
Holyer, J. Y. 1979 Large amplitude progressive interfacial waves. J. Fluid Mech. 93, 433.Google Scholar
Longuet-Higgins, M. S. & Gokelet, E. D. 1976 The deformation of steep surface waves on water. A numerical method of computation. Proc. R. Soc. Lond. A 350, 1.Google Scholar
Luke, J. C. 1967 A variational principle for a fluid with a free surface. J. Fluid Mech. 27, 395.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
Meiron, D. J. & Saffman, P. G. 1983 Overhanging gravity waves of large amplitude. J. Fluid Mech. 129, 213.Google Scholar
Miche, M. 1944 Mouvements ondulatoires de la mer en profondeur constante ou decroissant. Ann. Ponts Chaussees 114, 374.Google Scholar
Miles, J. W. 1986 Weakly nonlinear Kelvin–Helmholtz waves. J. Fluid Mech. 172, 513.Google Scholar
Milinazzo, F. A. & Saffman, P. G. 1990 Effect of a surface shear layer on gravity and gravity–capillary waves of permanent form. J. Fluid Mech. 216, 93.Google Scholar
Nayfeh, A. H. & Saric, W. S. 1972 Nonlinear waves in a Kelvin–Helmholtz flow. J. Fluid Mech 55, 311.Google Scholar
New, A. L., McIver, P. & Peregrine, D. H. 1985 Computations of overturning waves. J. Fluid Mech. 150, 233.Google Scholar
Pullin, D. I. & Grimshaw, R. H. J. 1983 Interfacial progressive gravity waves in a two-layer shear flow. Phys. Fluids 26, 1731.Google Scholar
Pullin, D. I. & Grimshaw, R. H. J. 1986 Stability of finite-amplitude interfacial waves. Part 3. The effect of basic current shear for one-dimensional instabilities. J. Fluid Mech. 172, 277.Google Scholar
Saffman, P. G. & Yuen, H. C. 1982 Finite-amplitude interfacial waves in the presence of a current. J. Fluid Mech. 123, 459.Google Scholar
Simmen, J. A. & Saffman, P. G. 1985 Steady deep-water waves on a linear shear current. Stud. Appl. Maths 73, 35.Google Scholar
Teles DA Silva, A. F. & Peregrine, D. H. 1988 Steep, steady surface waves on water of finite depth with constant vorticity. J. Fluid Mech. 195, 281.Google Scholar
Tsao, S. 1959 Behavior of surface waves on a linearly varying current. Mosk. Fiz. Tekh. Inst. Issled. Mekh. Prikl. Mat. 3, 66.Google Scholar
Whitham, G. B. 1974 linear and Nonlinear Waves. Wiley-lnterscience.