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Experimental and theoretical investigation of nonlinear sloshing waves in a rectangular channel

Published online by Cambridge University Press:  21 April 2006

E. Kit ,
L. Shemer  and
T. Miloh
E. Kit
Affiliation:
Faculty of Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel
L. Shemer
Affiliation:
Faculty of Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel
T. Miloh
Affiliation:
Faculty of Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel
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Abstract

Experimental and theoretical studies of sloshing waves in a rectangular channel in the vicinity of the second cutoff frequency are presented. The experiments were performed in a wave tank which is 1.2 m wide, 18 m long and 0.9 m deep. Sloshing waves were generated by a computer-controlled segmented wavemaker consisting of four independent modules. A sharp transition between two wave patterns, which exhibited hysteresis-type behaviour, was observed. At lower forcing frequencies a steady wave regime was obtained, while at higher frequencies modulation on a long timescale appeared. At stronger forcing, solitons were generated periodically at the wavemaker and then propagated away with a seemingly constant velocity. Experimental results are compared with numerical solutions of the appropriate nonlinear Schrödinger equation, a derivation of which is also presented. The importance of dissipation on the physical processes of wave evolution is discussed, and a simple dissipative model is suggested and incorporated in the governing equations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 181 , August 1987 , pp. 265 - 291
Copyright
© 1987 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., Mahony, J. J. & Pritchard, W. G. 1977 The excitation of surface waves near a cut-off frequency. Phil. Trans. R. Soc. Lond. A 286, 87–123.Google Scholar
Barnard, B. J. S. & Pritchard, W. G. 1972 Cross-waves. Part 2. Experiments. J. Fluid Mech. 55, 245–255.Google Scholar
Cox, E. A. & Mortell, M. P. 1986 The evolution of resonant water-wave oscillations. J. Fluid Mech. 162, 99–116.Google Scholar
Garrett, C. J. R. 1970 On cross-waves. J. Fluid Mech. 41, 837–849.Google Scholar
Larraza, A. & Putterman, S. 1984 Theory of non-propagating surface-wave solitons. J. Fluid Mech. 148, 443–449.Google Scholar
Lichter, S. & Shemer, L. 1986 Experiments on nonlinear cross waves. Phys. Fluids 29, 3971–3975.Google Scholar
Miles, J. W. 1976 Nonlinear surface waves in closed basins. J. Fluid Mech. 75, 419–448.Google Scholar
Miles, J. W. 1984 Parametrically excited solitary waves. J. Fluid Mech. 148, 451–460.Google Scholar
Miles, J. W. 1985 Note on parametrically excited trapped cross-wave. J. Fluid Mech. 151, 391–394.Google Scholar
Miloh, T. 1987 Weakly nonlinear resonant waves generated by an oscillatory pressure distribution in a channel. Wave Motion 9, 1–17.Google Scholar
Newman, J. N. 1977 Marine Hydrodynamics, pp. 247–248. MIT Press.
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
Schlichting, H. 1975 Boundary Layer Theory. McGraw-Hill.
Shemer, L., Kit, E. & Miloh, T. 1987 Measurements of two- and three-dimensional waves in a channel, including the vicinity of cut-off frequencies. Expt Fluids 5, 66–72.Google Scholar
Stakgold, L. 1979 Green's Function and Boundary Value Problems, pp. 207–214. J. Wiley.
Stiassnie, M. & Kroszynski, U. I. 1982 Long-time evolution of an unstable water-wave train. J. Fluid Mech. 116, 207–225.Google Scholar
Stiassnie, M. & Shemer, L. 1987 Energy computations for evolution of class I and II instabilities of Stokes waves. J. Fluid Mech. 174, 299–312.Google Scholar
Su, M.-Y. & Green, A. W. 1984 Coupled two- and three-dimensional instabilities of surface gravity waves. Phys. Fluids 27, 2595–2597.Google Scholar
Tadjbakhsh, L. & Keller, J. B. 1960 Standing surface waves of finite amplitude. J. Fluid Mech. 8, 442–451.Google Scholar
Ursell, F. 1952 Edge waves on a sloping beach. Proc. R. Soc. Lond. A 214, 79–97.Google Scholar
Wehausen, J. V. 1974 Methods for boundary-value problems in free-surface flows. The Third D. W. Taylor Lecture, DTNSRDC Rep. 4622. Bethesda, Maryland.Google Scholar
Wu, J., Keolian, R. & Rudnick, I. 1984 Observation of a nonpropagating hydrodynamic soliton. Phys. Rev. Lett. 52, 1421–1424.Google Scholar
Yuen, H. C. & Ferguson, W. E. 1978a Relationship between Benjamin—Feir instability and recurrence in the nonlinear Schrödinger equation. Phys. Fluids 21, 1275–1278.Google Scholar
Yuen, H. C. & Ferguson, W. E. 1978b Fermi—Pasta—Ulam recurrence in the two-space dimensional nonlinear Schrödinger equation. Phys. Fluids 21, 2116–2118.Google Scholar