Skip to main content
SpringerLink
Log in

Generation of unsteady waves by concentrated disturbances in an inviscid fluid with an inertial surface

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

The surface waves generated by unsteady concentrated disturbances in an initially quiescent fluid of infinite depth with an inertial surface are analytically investigated for two- and three-dimensional cases. The fluid is assumed to be inviscid, incompressible and homogenous. The inertial surface represents the effect of a thin uniform distribution of non-interacting floating matter. Four types of unsteady concentrated disturbances and two kinds of initial values are considered, namely an instantaneous/oscillating mass source immersed in the fluid, an instantaneous/oscillating impulse on the surface, an initial impulse on the surface of the fluid, and an initial displacement of the surface. The linearized initial-boundary-value problem is formulated within the framework of potential flow. The solutions in integral form for the surface elevation are obtained by means of a joint Laplace–Fourier transform. The asymptotic representations of the wave motion for large time with a fixed distance-to-time ratio are derived by using the method of stationary phase. The effect of the presence of an inertial surface on the wave motion is analyzed. It is found that the wavelengths of the transient dispersive waves increase while those of the steady-state progressive waves decrease. All the wave amplitudes decrease in comparison with those of conventional free-surface waves. The explicit expressions for the free-surface gravity waves can readily be recovered by the present results as the inertial surface disappears.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Maiti P., Mandal B.N.: Water waves generated by disturbances at an ice cover. Int. J. Math. Math. Sci. 2005, 737–746 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  2. Rhodes-Robinson P.F.: Note on the effect of surface tension on water waves at an inertial surface. J. Fluid Mech. 125, 375–377 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  3. Rhodes-Robinson P.F.: On the generation of water waves at an inertial surface. J. Aust. Math. Soc. B 25, 366–383 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  4. Mandal B.N.: Water waves generated by disturbance at an inertial surface. Appl. Sci. Res. 45, 67–73 (1988)

    Article  MATH  Google Scholar 

  5. Mandal B.N., Mukherjee S.: Water waves generated at an inertial surface by an axisymmetric initial surface disturbance. Int. J. Math. Educ. Sci. Technol. 20(5), 743–747 (1989)

    Article  MATH  Google Scholar 

  6. Pramanik A.K., Banik D.: The effect of inertial surface on capillary-gravity waves generated by a moving source. Indian J. Pure Appl. Math. 27(11), 1125–1135 (1996)

    MATH  Google Scholar 

  7. Kashiwagi M.: Research on hydroelastic responses of VLFS: Recent progress and future work. Int. J. Offshore Polar Eng. 10(2), 91–90 (2000)

    Google Scholar 

  8. Sahoo T., Yip T.L., Chwang A.T.: Scattering of surface waves by a semi-infinite floating elastic plate. Phys. Fluids 13(11), 3215–3222 (2001)

    Article  Google Scholar 

  9. Teng B., Cheng L., Li S.X. et al.: Modified eigenfunction expression methods for interaction of water waves with a semi-infinite elastic plate. Appl. Ocean Res. 23(6), 357–368 (2001)

    Article  Google Scholar 

  10. Squire V.A.: Of ocean waves and sea-ice revisited. Cold Regions Sci. Tech. 49(2), 110–133 (2007)

    Article  Google Scholar 

  11. Maiti P., Mandal B.N.: Water waves generated due to initial axisymmetric disturbance in water with an ice-cover. Arch. Appl. Mech. 74(9), 629–636 (2005)

    Article  MATH  Google Scholar 

  12. Lu D.Q., Dai S.Q.: Generation of transient waves by impulsive disturbances in an inviscid fluid with an ice-cover. Arch. Appl. Mech. 76(1-2), 49–63 (2006)

    Article  MATH  Google Scholar 

  13. Lu D.Q., Le J.C., Dai S.Q.: Unsteady waves due to oscillating disturbances in an ice-covered fluid. J. Hydrodyn. 18(3 Suppl.), 177–180 (2006)

    Article  Google Scholar 

  14. Lu D.Q., Le J.C., Dai S.Q.: Flexural-gravity waves due to transient disturbances in an inviscid fluid of finite depth. J. Hydrodyn. 20(2), 131–136 (2008)

    Article  Google Scholar 

  15. Stoker J.J.: Water Waves: the Mathematical Theory with Applications. Interscience, New York (1957)

    MATH  Google Scholar 

  16. Lighthill J.: Waves in Fluids. Cambridge University Press, Cambridge (1978)

    MATH  Google Scholar 

  17. Miles J.W.: The Cauchy–Poisson problem for a viscous liquid. J. Fluid Mech. 34, 359–370 (1968)

    Article  MATH  Google Scholar 

  18. Debnath L.: The linear and nonlinear Cauchy–Poisson wave problems for an inviscid or viscous liquid. In: Rassias, T.M. (eds) Topics in Mathematical Analysis, pp. 123–155. World Scientific, Singapore (1989)

    Google Scholar 

  19. Lu D.Q., Chwang A.T.: Free-surface waves due to an unsteady stokeslet in a viscous fluid of infinite depth. In: Cheng, L., Yeow, K. (eds) Proc. the 6th Int. Conf. Hydrodyn. Perth, Western Australia, pp. 611–617. Taylor & Francis Group, London (2004)

    Google Scholar 

  20. Chen X.B., Duan W.Y.: Capillary-gravity waves due to an impulsive disturbance. In: Clement, A.H., Ferrant, P. (eds) Proc. 18th Int. Workshop on Water Waves and Floating Bodies, Le Croisic, France, pp. 29–32. Ecole Centrale de Nantes, France (2003)

    Google Scholar 

  21. Lu, D.Q., Ng, C.O.: Interfacial capillary-gravity waves due to a fundamental singularity in a system of two semi-infinite fluids. J. Eng. Math. (2008). doi:10.1007/s10665-007-9199-6

  22. Dolai D.P.: Wave produced by disturbances at the interface between two superposed fluids. Proc. Indian Natn. Sci. Acad. A 62(2), 137–147 (1996)

    MATH  Google Scholar 

  23. Lu D.Q., Wei G., You Y.X.: Unsteady interfacial waves due to singularities in two semi-infinite inviscid fluids. J. Hydrodyn. B 17(6), 730–736 (2005)

    Google Scholar 

  24. Debnath L.: Nonlinear Water Waves. Academic Press, Boston (1994)

    MATH  Google Scholar 

  25. Debnath L.: On effect of viscosity on transient wave motions in fluids. Int. J. Eng. Sci. 7, 615–625 (1969)

    Article  MATH  Google Scholar 

  26. Miles J.W.: Transient gravity wave response to an oscillating pressure. J. Fluid Mech. 13, 145–150 (1962)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, 200072, Shanghai, China

    D. Q. Lu

  2. Shanghai Key Laboratory of Mechanics in Energy and Environment Engineering, 200072, Shanghai, China

    S. Q. Dai

Authors
  1. D. Q. Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Q. Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Q. Lu.

Additional information

The project supported by the National Natural Science Foundation of China (10602032), the Shanghai Rising-Star Program (07QA14022), and the Shanghai Leading Academic Discipline Project (Y0103).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lu, D.Q., Dai, S.Q. Generation of unsteady waves by concentrated disturbances in an inviscid fluid with an inertial surface. Acta Mech Sin 24, 267–275 (2008). https://doi.org/10.1007/s10409-008-0155-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-008-0155-0

Keywords

Search

Navigation