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Linear Instability of a Slowly Divergent Planar Jet

  • Polina Landa1
  • Vadim Ushakov
  • Jürgen Kurths
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 101)

Summary

By using small deviations from the stationary solution of the Navier-Stokes equation, the problem of linear instability of a plane submerged subsonic jet is considered. In the approximation of weak divergence of the jet, this problem reduces to a linear not self-adjoint boundary value problem with a given behavior of the variables at large values of the transversal coordinate. The solution of this boundary value problem allow us to calculate the gain factor and the phase velocity of hydrodynamical waves as functions of frequency and of distance from the nozzle. We have found that the dependence of the gain factor on the frequency has a resonant character. As the distance from the nozzle increases, the dependence of the gain factor on the frequency becomes more narrow and the maximum of that shifts into the small frequency region. Hence, the hydrodynamical waves become more and more coherent. The obtained results are in good agreement with experimental data.

Keywords

Phase Velocity Nozzle Exit Strouhal Number Longitudinal Velocity Gain Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Landa P S (1996) Europhys. Lett. 36:401CrossRefGoogle Scholar
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    Landa P S, Zaikin A A, Ginevsky A S and Vlasov Ye V (1999) Int. J. Bifurcation and Chaos 9:397CrossRefGoogle Scholar
  3. 3.
    Landau L D, Lifshitz E M (1986) Hydrodinamics. Naika, Moscow (in Russian)Google Scholar
  4. 4.
    Landa P S (1996) Nonlinear Oscillations and Waves in Dynamical Systems. Kluwer Academic Publ., DordrechtGoogle Scholar
  5. 5.
    Belotserkovsky S M, and Ginevsky A S (1995) Simulation of Turbulent Jets and Wakes by Dscrete Vortex Technique Nauka, Moscow (in Russian)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Polina Landa1
    • 1
  • Vadim Ushakov
    • 1
    • 2
  • Jürgen Kurths
    • 2
  1. 1.Department of PhysicsLomonosov Moscow State UniversityMoscowRussia
  2. 2.Nonlinear Dynamics GroupDepartment of Physics Potsdam UniversityPotsdamGermany

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