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Journal of Applied Mechanics and Technical Physics

, Volume 39, Issue 5, pp 699–709 | Cite as

Unsteady interaction of uniformly vortex flows

  • V. M. Teshukov
Article

Abstract

The problem of the decay of an arbitrary discontinuity (the Riemann problem) for the system of equations describing vortex plane-parallel flows of an ideal incompressible liquid with a free boundary is studied in a long-wave approximation. A class of particular solutions that correspond to flows with piecewise-constant vorticity is considered. Under certain restrictions on the initial data of the problem, it is proved that this class contains self-similar solutions that describe the propagation of strong and weak discontinuities and the simple waves resulting from the nonlinear interaction of the specified vortex flows. An algorithm for determining the type of resulting wave configurations from initial data is proposed. It extends the known approaches of the theory of one-dimensional gas flows to the case of substantially two-dimensional flows.

Keywords

Vorticity Riemann Problem Hydraulic Jump Secular Equation Simple Wave 
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.
    D. J. Benney, “Some properties of long waves,”Stud. Appl. Math.,52, 45–69 (1973).MATHGoogle Scholar
  2. 2.
    E. Varley and P. A. Blythe, “Long eddies in sheared flows,”Stud. Appl. Math.,68, 103–187 (1983).MATHMathSciNetADSGoogle Scholar
  3. 3.
    N. C. Freeman, “Simple waves on shear flows: similarity solutions,”J. Fluid Mech.,56, No. 2, 257–264 (1972).MATHMathSciNetCrossRefADSGoogle Scholar
  4. 4.
    P. A. Blythe, Y. Kazakia, and E. Varley, “The interaction of large amplitude shallow-water waves with an ambient flow,” —ibid., pp. 241–256.MATHCrossRefADSGoogle Scholar
  5. 5.
    V. M. Teshukov, “On the hyperbolicity of long-wave equations,”Dokl. Akad. Nauk SSSR,284, No. 3, 555–559 (1985).MATHMathSciNetGoogle Scholar
  6. 6.
    V. M. Teshukov, “Long waves in an eddying barotropic liquid,”Prikl. Mekh. Tekh. Fiz.,35, No. 6, 17–26 (1994).MATHMathSciNetGoogle Scholar
  7. 7.
    V. M. Teshukov, “Hydraulic jump in the shear flow of an ideal incompressible fluid,”Prikl. Mekh. Tekh. Fiz.,36, No. 1, 11–20 (1995).MATHMathSciNetGoogle Scholar
  8. 8.
    V. M. Teshukov, “Simple waves on a shear free-boundary flow of an ideal incompressible liquid,”Prikl. Mekh. Tekh. Fiz.,38, No. 2, 48–57 (1997).MATHMathSciNetGoogle Scholar
  9. 9.
    J. Smoller,Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, Berlin (1983).MATHGoogle Scholar
  10. 10.
    B. L. Rozhdestvenskii and N. N. Yanenko,Systems of Quasilinear Equations and Their Applications to Gas Dynamics [in Russian], Nauka, Moscow (1978).MATHGoogle Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • V. M. Teshukov

There are no affiliations available

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