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Long-time evolution and regions of existence of parametrically excited nonlinear cross-waves in a tank

Published online by Cambridge University Press:  26 April 2006

Lev Shemer  and
Eliezer Kit
Lev Shemer
Affiliation:
Department of Fluid Mechanics and Heat Transfer, Tel-Aviv University, Ramat-Aviv 69978, Israel
Eliezer Kit
Affiliation:
Department of Fluid Mechanics and Heat Transfer, Tel-Aviv University, Ramat-Aviv 69978, Israel
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Abstract

Results of an experimental and numerical study of parametrically excited nonlinear cross-waves in the vicinity of the cut-off frequency, are reported. Experiments are performed at three cross-wave modes and in the whole range of existence of cross-waves. Numerical studies are based on the solution of the nonlinear Schrödinger equation with a boundary condition at the wavemaker which corresponds to parametric excitation. The validity of the scaling procedure adopted in the model is verified experimentally. Dissipation is incorporated in the model equation and in the wavemaker boundary condition. The influence of the wave breaking on the range of existence of cross-waves is discussed and the relation between the maximum possible steepness of cross-waves and the limits of their existence is obtained.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 209 , December 1989 , pp. 249 - 263
Copyright
© 1989 Cambridge University Press

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References

Aranha, J. A., Yue, D. K. P. & Mei, C. C. 1982 Nonlinear waves near a cut-off frequency in an acoustic duct—a numerical study. J. Fluid Mech. 121, 465–485.Google Scholar
Barnard, B. J. S. & Pritchard, W. G. 1972 Cross-waves. Part 2. Experiments. J. Fluid Mech. 55, 245–255.Google Scholar
Garrett, C. J. R. 1970 On cross-waves. J. Fluid Mech. 41, 837–849.Google Scholar
Havelock, T. H. 1929 Forced surface waves on water. Phil. Mag. 8, 569–576.Google Scholar
Hocking, L. M. 1987 The damping of capillary—gravity waves at a rigid boundary. J. Fluid Mech. 179, 253–266.Google Scholar
Jones, A. F. 1984 The generation of cross-waves in a long deep channel by parametric resonance. J. Fluid Mech. 138, 53–74.Google Scholar
Kit, E. & Shemer, L. 1989 On the neutral stability of cross-waves. Phys. Fluids A 1, 1128–1132.Google Scholar
Kit, E., Shemer, L. & Miloh, T. 1987 Experimental and theoretical investigation of nonlinear sloshing waves in a rectangular channel. J. Fluid Mech. 181, 265–291.Google Scholar
Lichter, S. & Chen, J. 1987 Subharmonic resonance of nonlinear cross-waves. J. Fluid Mech. 183, 451–465.Google Scholar
Lichter, S. & Shemer, L. 1986 Experiments on nonlinear cross waves. Phys. Fluids 29, 3971–3975.Google Scholar
Mahony, J. J. 1972 Cross-waves. Part I. Theory. J. Fluid Mech. 55, 229–244.Google Scholar
Mei, C. C. & Liu, L. F. 1973 The damping of surface gravity waves in a bounded liquid. J. Fluid Mech. 59, 239–256.Google Scholar
Miles, J. W. 1984 Parametrically excited solitary waves. J. Fluid Mech. 148, 451–460.Google Scholar
Miles, J. W. 1985 Note on a parametrically excited, trapped cross-wave. J. Fluid Mech. 151, 391–394.Google Scholar
Miles, J. W. & Becker, J. 1988 Parametrically excited, progressive cross-waves. J. Fluid Mech. 186, 129–146.Google Scholar
Penney, W. G. & Price, H. T. 1952 Part II. Finite periodic stationary gravity waves in a perfect fluid. Phil. Trans. R. Soc. Lond A 244, 254–284.Google Scholar
Shemer, L. & Lichter, S. 1987 Identification of cross-wave regimes in the vicinity of a cut-off frequency. Phys. Fluids 30, 3427–3433.Google Scholar
Shemer, L. & Kit, E. 1988 Study of the role of dissipation in evolution of nonlinear sloshing waves in a rectangular channel. Fluid Dyn. Res. 4, 89–105.Google Scholar
Shemer, L., Kit, E. & Miloh, T. 1987 Measurements of two-and three-demensional waves in a channel, including the vicinity of cut-off frequencies. Exps Fluids 5, 66–72.Google Scholar