Advertisement

Journal of Hydrodynamics

, Volume 18, Issue 1, pp 170–175 | Cite as

Gravity waves with effect of surface tension and fluid viscosity

  • Xiao-Bo Chen
  • Wen-Yang Duan
  • Dong-Qiang Lu
Session A3

Abstract

The potential flow in a viscous fluid due to a point impulsive source is considered within the framework of linear Stokes equations. The combined effect of fluid viscosity and surface tension on the potential function below and on the water surface is studied. Dependent on the wavenumbers associated with the level of the effect due to surface tension, the oscillations can be grouped as gravity-dominant waves and capillary-dominant waves. It is shown that the wave form of gravity-dominant oscillations is largely modified by the surface tension while the wave amplitude of capillary-dominant oscillations is mostly reduced by the fluid viscosity.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Abramowitz M. & Stegun I.A. (1967) Hand-book of mathematical functions. Dover Publications.Google Scholar
  2. [2]
    Chen X.B. & Wu G.X. (2001) On singular and highly oscillatory properties of the Green function for ship motions. J. Fluid Mech. 445, 77–91.MathSciNetCrossRefGoogle Scholar
  3. [3]
    Chen X.B. (2002) Role of surface tension in modelling ship waves. Proc. 17th Intl Workshop on Water Waves and Floating Bodies, Cambridge (UK), 25–28.Google Scholar
  4. [4]
    Chen X.B. & Duan W.Y. (2003) Capillary-gravity waves due to an impulsive disturbance. Proc. 18th Intl Workshop on Water Waves and Floating Bodies, Carry-Le-Rouet (France)Google Scholar
  5. [5]
    Chen X.B., Lu D.Q., Duan W.Y. & Chwang A.T. (2006) Potential flow below the capillary surface of a viscous fluid. Proc. 21st Intl Workshop on Water Waves and Floating Bodies, Loughborough (UK)Google Scholar
  6. [6]
    Clément A.H. (1998) An ordinary differential equation for the Green function of time-domain free-surface hydrodynamics. J. Eng. Math. 33(2), 201–217.MathSciNetCrossRefGoogle Scholar
  7. [7]
    Crapper G.D. (1964) Surface waves generated by a travelling pressure point. Proc. Royal Soc. London A, 282, 547–558.MathSciNetCrossRefGoogle Scholar
  8. [8]
    Lamb H. (1932) Hydrodynamics. 6th Ed. Dover Publications, New York.zbMATHGoogle Scholar
  9. [9]
    Lu D.Q. & Chwang A.T. (2004) Free-surface waves due to an unsteady Stokeslet in a viscous fluid of infinite depth. Proc. 6th ICHD, 611–17.Google Scholar
  10. [10]
    Miles J.W. (1968) The Cauchy-Poisson problem for a viscous liquid. J. Fluid Mech. 34, 359–70.CrossRefGoogle Scholar
  11. [12]
    Wehausen J.V. & Laitone E.V. (1960) Surface waves. Handbuch des Physik Springer-Verlag.CrossRefGoogle Scholar
  12. [13]
    Yih C.S. & Zhu S. (1989) Patterns of ship waves II: gravity-capillary waves. Q. Appl. Math. 47 35–44.MathSciNetCrossRefGoogle Scholar
  13. [14]
    Zilman G. & Miloh T. (2001) Kelvin and V-like ship waves affected by surfactants. J. Ship Res. 45, 2, 150–163.Google Scholar

Copyright information

© China Ship Scientific Research Center 2006

Authors and Affiliations

  1. 1.Research DepartmentBVParisFrance
  2. 2.College of Shipbuilding EngineeringHEUHarbinChina
  3. 3.Shanghai Institute of Applied Mathematics and MechanicsSHUShanghaiChina

Personalised recommendations