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Journal of Engineering Mathematics

, Volume 40, Issue 1, pp 77–90 | Cite as

The effect of viscosity on the transient free-surface waves in a two-dimensional tank

  • G.X. Wu
  • R. Eatock Taylor
  • D.M. Greaves
Article

Abstract

The paper attempts to develop some understanding of the interaction between viscous flow and a free surface by analysing the unsteady flow in an idealised two-dimensional rectangular tank. The mathematical model used is based on the linearized Navier-Stokes equations which are solved by use of the Laplace transform. Various results are provided to show the effect of viscosity on the free surface waves.

free surface sloshing waves viscosity 

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References

  1. 1.
    M. J. Lighthill, Waves in Fluids. Cambridge: CUP (1978) 504 p.Google Scholar
  2. 2.
    T. Sarpkaya and M. Issacson, Mechanics of Wave Forces on Offshore Structures. New York: Van Nostrand (1981) 651 p.Google Scholar
  3. 3.
    R.W. Yeung and X. Yu, Wave-structure interaction in a viscous fluid. Fourteenth Int. Conf. on Offshore Mech & Arctic Eng, Copenhagen (Denmark) (1995).Google Scholar
  4. 4.
    C. C. Mei, The Applied Dynamics of Ocean Surface Waves. New York: Wiley-Interscience (1983) 740 p.Google Scholar
  5. 5.
    H. Lamb, Hydrodynamics (6th edition). Cambridge: CUP (1976) 738 p.Google Scholar
  6. 6.
    Q. Chen, E. Rame and S. Garoff, The velocity field near a moving contact line. J. Fluid Mech. 337 (1997) 49–66.Google Scholar
  7. 7.
    E. A. Cerda and E. L. Tirapegui, Faraday's instability in viscous fluid. J. Fluid Mech. 368 (1998) 195–228.Google Scholar
  8. 8.
    C. Y. Loh and H. Rasmussen, A numerical procedure for viscous free surface flow. Appl. Num. Math. 3 (1987) 479–495.Google Scholar
  9. 9.
    T. B. Benjamin and F. Ursell, The stability of the plane free surface of a liquid in a vertical periodic motion. Proc. R. Soc. London A225 (1954) 505–515.Google Scholar
  10. 10.
    G. X. Wu and R. Eatock Taylor, Finite element analysis of two-dimensional non-linear transient water waves. Appl. Ocean Res. 16 (1994) 363–372.Google Scholar
  11. 11.
    M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York: Dover (1965) 1043 p.Google Scholar
  12. 12.
    O. M. Faltinsen, A numerical non-linear method of sloshing in tanks with two-dimensional flow. J. Ship Res. 18 (1978) 224–241.Google Scholar
  13. 13.
    G. X. Wu, Q. W. Ma and R. Eatock Taylor, Numerical simulation of sloshing waves in a 3D tank based on a finite element method. Appl. Ocean Res. 20 (1998) 337–355.Google Scholar
  14. 14.
    S. Somalinga and A. Bose, Numerical investigation of boundary conditions formoving contact line problems. Phys. Fluids 12 (2000) 499–510.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • G.X. Wu
    • 1
  • R. Eatock Taylor
    • 2
  • D.M. Greaves
    • 1
  1. 1.Department of Mechanical EngineeringUniversity College LondonLondon UK
  2. 2.Department of Engineering ScienceUniversity of OxfordOxford UK

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