Skip to main content
SpringerLink
Log in

Perturbations on interfaces between media driven by the vertical ascent of a circular cylinder in a multilayer fluid

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

The initial-boundary value problem of the vertical ascent of a circular cylinder in a multilayer fluid is considered within the nonlinear theory. In each layer the fluid is ideal, incompressible, heavy, and homogeneous. At the initial instant of time the cylinder is located in the lower layer and begins smoothly to accelerate vertically from zero to a constant velocity. A system of integrodifferential equations of the problem is obtained. As unknowns, this system contains both the intensities of the singularities simulating the fluid and rigid boundaries and the functions describing the shape of the interface between the fluid media. The numerical solution of this system is based on two iteration processes, one of which is associated with time integration using the Runge-Kutta-Felberg scheme, while the other is associated with the solution of a system of linear algebraic equations obtained by discretization of the integral relations in each time step. The problem of the vertical ascent of a cylinder in a three-layer fluid (seawater, fresh water and air) is considered in detail. The results of calculating the perturbations of the fluid interfaces and the distributed and total hydrodynamic contour characteristics are given. The results obtained are compared with the solution of the problem of the ascent of a circular cylinder to the interface between water and air media. It is concluded that the third layer and the Froude number significantly affect the nature of the perturbations induced by the contour.

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. S. I. Gorlov, “Numerical methods of solving nonlinear time-dependent problems of wave generation by a body submerged in a fluid,”Vychisl. Tekhnologii,3, No. 6, 9 (1998).

    MATH  MathSciNet  Google Scholar 

  2. A. G. Terentiev, K. E. Afanasiev, and M. M. Afanasieva, “Simulation of unsteady free surface flow problems by direct boundary element method,” in:Advanced Boundary Element Methods: IUTAM Symp., Springer, San Antonio, Berlin at el. (1988), P. 427.

    Google Scholar 

  3. J. G. Telste, “Inviscid flow about a cylinder rising to a free surface,”J. Fluid Mech.,182, 149 (1987).

    Article  MATH  ADS  Google Scholar 

  4. M. Greenhow, “Water entry and exit of a horizontal circular cylinder,”Appl. Ocean. Res.,10, No. 4, 191 (1988).

    Article  Google Scholar 

  5. P. A. Tyvand and T. Miloh, “Free-surface flow due to impulsive motion of a submerged circular cylinder,”J. Fluid Mech.,286, 67 (1995).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. P. A. Tyvand and T. Miloh. “Free-surface flow generated by a small submerged circular cylinder starting from rest,”J. Fluid Mech.,286, 103 (1995).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. M. Greenhow and S. Moyo, “Water entry and exit of horizontal circular cylinders,”Phil. Trans. Roy. Soc. London, Ser. A.,355, No. 1724, 551 (1997).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  8. S. Moyo,Hydrodynamic Interaction of Horizontal Circular Cylinders with a Free Surface, Ph. Thesis, Brunel Univ. (1997).

  9. I. R. Park and H. H. Chun, “Analysis of flow around a rigid body in water-entry and exit problems by a finite volume method,” in:6th Symp. on Nonlinear and Free-Surface Flows, Hiroshima (1998).

  10. G. E. Forsythe, M. M. Malcolm, and C. B. Moler,Computer Methods for Mathematical Computations, Prentice-Hall, Englewood Cliffs (1977).

    MATH  Google Scholar 

  11. J. L. Hess, “Higher-order numerical solution of the integral equation for the two-dimensional Neumann problem,”Comput. Meth. Appl. Mech. and Engng.,2, No. 1, 1 (1973).

    Article  MATH  Google Scholar 

  12. G. R. Baker, D. I. Meiron, and S. A. Orszag, “Application of a generalized vortex method to nonlinear free-surface flows,” in:Proc. 3rd Intern. Conf. on Numerical Ship Hydrodynamics, Paris (1981).

  13. M. S. Longuet-Higgins and E. D. Cokelet, “The deformation of steep surface waves on water. I. A numerical method of computation,”Proc. Roy. Soc. London, Ser. A.,350, No. 1660, 1 (1976).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  14. R. Shapiro, “Linear filtering,”Math. Comput.,29, No. 132, 1094 (1975).

    Article  MATH  Google Scholar 

  15. O. M. Faltisen,Sea Loads on Ships and Offshore Structures, Univ. Press, Cambridge (1990).

    Google Scholar 

Download references

Authors
  1. S. I. Gorlov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Omsk, e-mail: gorlov@iitam.omsk.net.ru. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 153–159, March–April, 2000.

The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 96-01-00093).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gorlov, S.I. Perturbations on interfaces between media driven by the vertical ascent of a circular cylinder in a multilayer fluid. Fluid Dyn 35, 282–287 (2000). https://doi.org/10.1007/BF02831437

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02831437

Keywords

Search

Navigation