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An experimental note on finite-amplitude standing gravity waves

Published online by Cambridge University Press:  28 March 2006

Dave Fultz
Affiliation:
Hydrodynamics Laboratory, Department of the Geophysical Sciences, University of Chicago

Abstract

In a recent paper Tadjbakhsh & Keller (1960) have predicted that two-dimensional finite standing gravity waves in a rectangular container will have lower frequency than infinitesimal standing waves in deep water but have higher frequency below a certain mean depth to wavelength ratio. This is in strong contrast to the frequency results for finite progressive waves obtained by many investigators. Experimental confirmation of this prediction is reported together with estimates of the magnitude of the frequency effects at several depths. The frequency effect reversal appears to occur at a depth ratio of 0·14, somewhat less than the predicted ratio of 0·17.

Type
Research Article
Copyright
© 1962 Cambridge University Press

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References

Case, K. M. & Parkinson, W. C. 1957 Damping of surface waves in an incompressible liquid. J. Fluid Mech. 2, 17284.Google Scholar
Cooper, R. M. 1960 Dynamics of liquids in moving containers. Amer. Rocket Soc. J., 30, 7259.Google Scholar
Forel, F. A. 1876 La formule des seiches. Arch. Sci. Phys. Natur. Geneve, 57, 27892.Google Scholar
Guthrie, F. 1875 On stationary liquid waves. Phil. Mag. (4), 50, 290302, 37788.Google Scholar
Honda, K. & Matsushita, T. 1913 An investigation of the oscillations of tank-water. Sci. Rep. Tohoku Imp. Univ., Sendai (1), 2, 13148.Google Scholar
Keulegan, G. H. 1959 Energy dissipation in standing waves in rectangular basins. J. Fluid Mech., 6, 3350.Google Scholar
Kirchhoff, G. & Hansemann, G. 1880 Versuche über stehende Schwingungen des Wassers. Ann. Phys. Chem. 10, 33747; Gesammelte Abhandlungen, pp. 442-54, 1882. Leipzig: J. A. Barth.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th ed., p. 364 ff. and p. 440 ff. Cambridge University Press.
Lechat, F.-H. 1880 Des vibrations à la surface des liquides. Ann. Chim. Phys. (5), 19, 289344.Google Scholar
Lin, J. D. & Howard, L. N. 1960 Nonlinear standing waves in a rectangular tank due to forced oscillation. Tech. Rep. 44 MIT Hydrodynamics Lab., ONR contracts Nonr 1841-12 and 1841 (65).Google Scholar
Merian, J. R. 1828 über die bewegung tropfbarer Flüssigkeiten in Gefässen. Basle.
Moiseyev, N. N. 1958 On the theory of nonlinear vibrations of a liquid of finite volume. Prikl. Mat. Mekh. 22, 61221 (in Russian).Google Scholar
Penney, W. G. & Price, A. T. 1952 Some gravity wave problems in the motion of perfect liquids. Part II. Finite periodic stationary gravity waves in a perfect liquid. Phil. Trans. A, 244, 25484.Google Scholar
Rankine, W. J. M. 1865 Supplement to a paper on stream-lines. Phil. Mag. (4), 29, 258.Google Scholar
Rayleigh, Lord 1876 On waves. Phil. Mag. (5), 1, 25779.Google Scholar
Stokes, Sir G. G. 1880 Considerations relative to the greatest height of oscillatory waves which can be propagated without change of form. Math. Phys. Pap. 1, 2258.Google Scholar
Tadjbakhsh, I. & Keller, J. B. 1960 Standing surface waves of finite amplitude. J. Fluid Mech. 8, 44251.Google Scholar
Taylor, Sir G. 1953 An experimental study of standing waves. Proc. Roy. Soc. A, 218, 4459.Google Scholar
Ursell, F., Dean, R. G. & Yu, Y. S. 1960 Forced small-amplitude water waves: a comparison of theory and experiment. J. Fluid Mech. 7, 3352.Google Scholar
White, P. & Watson, W. 1905-06 Some experimental results in connection with the hydrodynamical theory of seiches. Proc. Roy. Soc. Edinb. 26, 14356.Google Scholar