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Free-surface oscillations of fluid in closed basins

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Abstract

The mild-slope equation, well-known in wave refraction theory, is used to calculate the natural frequencies of oscillation of fluid in a basin. The method may be applied to canals of variable cross-section and to axisymmetric basins provided that every point in the fluid lies directly beneath the free surface. Comparison is made with previously known solutions and some new results are presented for axisymmetric geometries.

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References

  1. N.N. Moiseev and A.A. Petrov, The calculation of free oscillations in a motionless container, Advances in Applied Mechanics 9 (1965) 91–154.

    Google Scholar 

  2. D.W. Fox and J.R. Kuttler, Sloshing frequencies, J. Applied. Maths. and Physics (Z.A.M.P.) 34 (1983) 668–696.

    Google Scholar 

  3. H. Lamb, Hydrodynamics, 6th edition, Cambridge University Press (1932).

  4. J.W. Miles, Surface waves in basins of variable depth, J. Fluid Mech. 152 (1985) 379–389.

    Google Scholar 

  5. C.C. Mei, The Applied Dynamics of Ocean Surface Waves, Wiley-Interscience (1983).

  6. R. Smith and T. Sprinks, Scattering of surface waves by a conical island, J. Fluid Mech. 72 (1975) 373–384.

    Google Scholar 

  7. P. McIver and D.V. Evans, The trapping of surface waves above a submerged, horizontal cylinder, J. Fluid Mech. 151 (1985) 243–255.

    Google Scholar 

  8. C.M. Bender and S.A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill (1978).

  9. S.R. Smith, Numerical solution of a Sturm-Liouville eigenvalue problem, Undergraduate Project Report, Brunel University (1986).

  10. J.R. Kuttler and V.G. Sigillito, Sloshing of liquids in cylindrical tanks, American Inst. of Aeronautics and Astronautics J. 22 (1984) 309–311.

    Google Scholar 

  11. S.C. Chang and S.T. Wu, On the natural frequencies of standing waves in a canal of arbitrary shape, J. Applied Math. and Physics (Z.A.M.P.) 23 (1972) 881–888.

    Google Scholar 

  12. B. Budiansky, Sloshing of liquids in circular canals and spherical tanks, J. Aerospace Sciences 27 (1960) 161–173.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Brunel University, Uxbridge, UB8 3PH, Middlesex, England

    P. McIver & S. R. Smith

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  1. P. McIver
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  2. S. R. Smith
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McIver, P., Smith, S.R. Free-surface oscillations of fluid in closed basins. J Eng Math 21, 139–148 (1987). https://doi.org/10.1007/BF00127671

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  • DOI: https://doi.org/10.1007/BF00127671

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