Fluid Dynamics

, Volume 53, Issue 2, pp 285–295 | Cite as

Nonlinear Instability in the Region of Laminar-Turbulent Transition in Supersonic Three-Dimensional Flow over a Flat Plate

  • I. I. LipatovEmail author
  • R. Ya. Tugazakov


Direct numerical simulation is applied to obtain laminar-turbulent transition in supersonic flow over a flat plate. It is shown that, due to the nonlinear instability, Tollmien–Schlichting waves generated in the boundary layer lead to the formation of oblique disturbances in the flow. These represent a combination of compression and expansion waves, whose intensities can be two orders higher than that of external harmonic disturbances. The patterns of the three-dimensional flow over the plate are presented and the structures of the turbulent flat-plate boundary layers are described for the freestream Mach numbers M = 2 and 4.


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  1. 1.
    S.A. Gaponov and A.A. Maslov, Disturbance Development in Compressible Flows [in Russian] (Nauka, Novosibirsk, 1980).Google Scholar
  2. 2.
    O.M. Belotserkovskii, ConstructiveModeling of Structural Turbulence and Hydrodynamic Instabilities (World Sci., Singapore, 2009).CrossRefzbMATHGoogle Scholar
  3. 3.
    V.V. Kozlov, G.R. Grek, L.L. Lefdal, V.G. Chernorai, and M.V. Litvinenko, “Role of Streamwise Localized Structures in Transition to Turbulence in Boundary Layers and Jets (an Overview),” Zh. Prikl.Mekh. Tekhn. Fiz. 43 (2), 62 (2002).Google Scholar
  4. 4.
    A.D. Kosinov, A.V. Panina, G.L. Kolosov, N.V. Semionov, and Yu.G. Ermolaev, “Experiments on Relative Receptivity of Three-Dimensional Supersonic Boundary Layer to Controlled Disturbances and its Development,” Progress in Flight Physics 5, 69 (2013).CrossRefGoogle Scholar
  5. 5.
    I.I. Lipatov and R.Ya. Tugazakov, “Phenomenon of Formation of Pressure Pulsations during the Shock Waves on the Boundary Layer,” TsAGI Sci. J. 44 (1), 93 (2013).CrossRefGoogle Scholar
  6. 6.
    I.I. Lipatov and R.Ya. Tugazakov, “Generation of Coherent Structures in Supersonic Flow past a Finite-Span Flat Plate,” Fluid Dynamics 50 (6), 793 (2015).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    V.N. Brazhko, “Periodic Structure of Flow and Heat Transfer in the Region of Supersonic Flow Reattachment,” Uch. Zap. TsAGI 10 (2), 113 (1979).Google Scholar
  8. 8.
    G.F. Glotov, “Distinctive Features of Generation and Development of Recirculation Flow Zones in Shear Layers of Supersonic Flows,” Zh. Prikl.Mekh. Tekhn. Fiz. 36 (5), 30 (1995).Google Scholar
  9. 9.
    L.R. Ephraim and S.Z. Burstein, “Difference Methods for the Inviscid and Viscous Equations of a Compressible Gas,” J. Comput. Phys. 2, 178 (1967).ADSCrossRefGoogle Scholar
  10. 10.
    R.Ya. Tugazakov, “On the Theory of Supersonic Inviscid Flow Separation in Gasdynamic Problems,” Fluid Dynamics 51 (5), 689 (2016).MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    L.L. Landau and E. MLifshitz, Fluid Mechanics (Pergamon, London, 1987).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Central Aerohydrodynamic Institute (TsAGI)Zhukovsky, Moscow oblastRussia

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