Stationary Binnie waves near resonance
Author:
Songping Zhu
Journal:
Quart. Appl. Math. 50 (1992), 585-597
MSC:
Primary 76B15
DOI:
https://doi.org/10.1090/qam/1178436
MathSciNet review:
MR1178436
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Abstract: Stationary waves in an open channel with corrugated side walls possess resonant speeds at or near which the prediction of free surface waves by the linear approximation fails. However, if the nonlinear terms in the Euler equation and boundary conditions are kept, a finite amplitude of these stationary waves can be determined. In this paper, such a nonlinear approach is presented, and the amplitude of the waves near the resonant speeds is determined to be of the order of the one-third power of the side-wall corrugation amplitude.
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J. A. Aranha, D. K. P. Yue, and C. C. Mei, Nonlinear waves near a cut-off frequency in an acoustic duct—a numerical study, J. Fluid Mech. 121, 465–485 (1982)
R. Betchov, Nonlinear oscillations of a column of gas, Phys. Fluids 1, 205–212 (1958)
A. M. Binnie, Self-induced waves in a conduit with corrugated walls. I. Experiments with water in an open horizontal channel with vertically corrugated sides, Proc. Roy. Soc. London Ser. A 259, 18–27 (1960)
B.-T. Chu and S. J. Ying, Thermally driven nonlinear oscillations in a pipe with travelling shock waves, Phys. Fluids 6, 1625–1637 (1963)
W. Chester, Resonant oscillations of water waves, Proc. Roy. Soc. London Ser. A 306, 5–22 (1968)
G. Dagan and T. Miloh, Free-surface flow past oscillating singularities at resonant frequency, J. Fluid Mech. 120, 139–154 (1982)
W. Ellermeier, Resonant surface waves over a wavy bottom, Personal communication, 1983
A. F. Jones, The generation of cross-waves in a long deep channel by parametric resonance, J. Fluid Mech. 138, 53–74 (1984)
H. Lamb, Hydrodynamics, 6th ed., Cambridge University Press, Cambridge, 1945
J. R. Ockendon and H. Ockendon, Resonant surface waves, J. Fluid Mech. 59, 397–413 (1973)
C.-S. Yih, Binnie waves, 14th Sympos. on Naval Hydrodynamics, Ann. Arbor, Michigan, 1982
C.-S. Yih, Waves in meandering streams, J. Fluid Mech. 130, 109–121 (1983)
S.-P. Zhu, Open channel flows near the resonance speed, Ph.D. thesis, Univ. Michigan, Ann. Arbor, 1987
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Article copyright:
© Copyright 1992
American Mathematical Society
