Skip to main content
SpringerLink
Log in

Evolution equation for weakly nonlinear waves in a two-layer fluid with gently sloping bottom and lid

  • Published:
Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

A second-order differential model for three-dimensional perturbations of the interface of two fluids of different density is constructed. An evolution equation for traveling quasistationary waves of arbitrary length and small but finite amplitude is obtained. In the case of the horizontal bottom and lid, there are perturbations of the Stokes-wave type among steady-state periodic solutions. For moderately long perturbations, solutions in the form of solitary waves which are in agreement with the available experimental and analytical results are found. The problem of a smooth transition from the deep-fluid to the shallow-fluid region is studied.

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. A. A. Borisov and G. A. Khabakhpashev, “Propagation of weakly nonlinear disturbances of the interface between two layers of fluid”,Izv. Akad. Nauk, Mekh. Zhidk, Gaza, No. 1, 125–131 (1994).

    MATH  Google Scholar 

  2. G. Lamb,Hydrodynamics, Cambridgr Univ. Press, (1931).

  3. N. V. Gavrilov, “Viscous attenuation of solitary internal waves a two-layer fluid”,Prikl. Mekh. Tekh. Fiz., No. 4, 51–55 (1988).

    Google Scholar 

  4. S. A. Thorpe, “On the shape of progressive internal waves”,Philos. Trans. Roy. Soc, London, Ser. A,263, 563–614 (1968).

    MATH  ADS  Google Scholar 

  5. J. S. Turner,Buoyancy Effects in Fluids, Cambridge Univ. Press (1973).

  6. V. D. Djordjevic and L. G. Redecopp, “The fission and disintegration of internal solitary waves moving over two-dimensional topography”,J. Phys. Oceanogr.,8, No. 6, 1016–1024 (1978).

    Article  ADS  Google Scholar 

  7. G. A. Khabkhpashev, “Evolution of disturbances of the interface between two layers of viscous fluid”,Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, No. 6, 118–123 (1990).

    Google Scholar 

  8. R. R. Long, “Solitary waves in one- and two-fluid systems”,Tellus,8, No. 4, 460–471 (1990).

    Article  Google Scholar 

  9. T. B. Benjamin, “Internal waves of finite amplitude and permanent form”,J. Fluid Mech.,25, No. 2, 241–270 (1966).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  10. E. N. Pelinovsky, “A ‘differential’ model of waves on water”,Dokl. Ross. Akad. Nauk,300, No. 5, 1231–1234 (1988).

    Google Scholar 

Download references

Authors
  1. G. A. Khabakhpashev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. Yu. Tsvelodub
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 62–72. September–October, 1999.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Khabakhpashev, G.A., Tsvelodub, O.Y. Evolution equation for weakly nonlinear waves in a two-layer fluid with gently sloping bottom and lid. J Appl Mech Tech Phys 40, 831–840 (1999). https://doi.org/10.1007/BF02468466

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02468466

Keywords

Search

Navigation