Technical Physics Letters

, Volume 42, Issue 9, pp 886–890 | Cite as

Describing the motion of a body with an elliptical cross section in a viscous uncompressible fluid by model equations reconstructed from data processing

  • A. V. Borisov
  • S. P. Kuznetsov
  • I. S. Mamaev
  • V. A. Tenenev
Article

Abstract

From analysis of time series obtained on the numerical solution of a plane problem on the motion of a body with an elliptic cross section under the action of gravity force in an incompressible viscous fluid, a system of ordinary differential equations approximately describing the dynamics of the body is reconstructed. To this end, coefficients responsible for the added mass, the force caused by the circulation of the velocity field, and the resisting force are found by the least square adjustment. The agreement between the finitedimensional description and the simulation on the basis of the Navier–Stokes equations is illustrated by images of attractors in regular and chaotic modes. The coefficients found make it possible to estimate the actual contribution of different effects to the dynamics of the body.

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References

  1. 1.
    A. Andersen, U. Pesavento, and Z. Wang, J. Fluid Mech. 541, 65 (2005).ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Y. Tanabe and K. Kaneko, Phys. Rev. Lett. 73, 1372 (1994).ADSCrossRefGoogle Scholar
  3. 3.
    A. Belmonte, H. Eisenberg, and E. Moses, Phys. Rev. Lett. 81, 345 (1998).ADSCrossRefGoogle Scholar
  4. 4.
    S. P. Kuznetsov, Regul. Chaot. Dyn. 20, 345 (2015).ADSCrossRefGoogle Scholar
  5. 5.
    S. M. Aul’chenko, V. O. Kaledin, and Yu. V. Shpakova, Tech. Phys. Lett. 35, 114 (2009).ADSCrossRefGoogle Scholar
  6. 6.
    E. V. Vetchanin, I. S. Mamaev, and V. A. Tenenev, Reg. Chaot. Dyn. 18, 100 (2013).MathSciNetCrossRefGoogle Scholar
  7. 7.
    S. M. Ramodanov and V. A. Tenenev, Nelin. Dinam. 7, 635 (2011).CrossRefGoogle Scholar
  8. 8.
    V. V. Kozlov and S. M. Ramodanov, J. Appl. Math. Mech. 65, 579 (2001).MathSciNetCrossRefGoogle Scholar
  9. 9.
    S. M. Ramodanov, V. A. Tenenev, and D. V. Treschev, Regul. Chaot. Dyn. 17, 547 (2012).ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    A. A. Kilin and E. V. Vetchanin, Nelin. Dinam. 11, 633 (2015).CrossRefGoogle Scholar
  11. 11.
    V. V. Kozlov, Vestnik MGU. Ser. 1: Mat. Mekh., No. 1, 79 (1990).Google Scholar
  12. 12.
    B. P. Bezruchko and D. A. Smirnov, Extracting Knowledge from Time Series: An Introduction to Nonlinear Empirical Modeling (Springer, Berlin, 2010).CrossRefMATHGoogle Scholar
  13. 13.
    S. P. Kuznetsov, Dynamic Chaos (Fizmatlit, Moscow, 2006) [in Russian].MATHGoogle Scholar
  14. 14.
    L. I. Sedov, Planar Problems of Hydrodynamics and Mechanics (Nauka, Moscow, 1966).Google Scholar
  15. 15.
    A. V. Borisov and I. S. Mamaev, Chaos 16, 013118 (2006).ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  • A. V. Borisov
    • 1
  • S. P. Kuznetsov
    • 1
    • 3
  • I. S. Mamaev
    • 1
    • 2
  • V. A. Tenenev
    • 2
  1. 1.Udmurt State UniversityIzhevskRussia
  2. 2.Izhevsk State Technical UniversityIzhevskRussia
  3. 3.Institute of Radio-Engineering and Electronics, Saratov BranchRussian Academy of SciencesSaratovRussia

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