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Role of Non-Wave-Like Disturbances in Transition

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Waves and Nonlinear Processes in Hydrodynamics

Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 34))

Abstract

How disturbances evolve in a shear flow of small viscosity has been a problem at the center of transition research from the early beginning of that field of inquiry since Rayleigh (1880) showed that for an inviscid parallel shear flow a necessary condition for an infinite wave train to grow exponentially with time is the presence of an inflection point in the shear flow. Fjørtoft (1950) was able to sharpen Rayleigh’s criterion by demonstrating that the instability occurs only for a maximum in the shear rate. Most of the investigations to date have focused on how Tollmien-Schlichting wave-like disturbances evolve in time and space. However, as Gustavsson (1981) and others have pointed out, discrete wave modes do not provide a complete description of the disturbance flow field in a boundary layer, but a continuous set must also be included which may be of increasing importance as the viscosity becomes smaller

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References

  • Ellingsen, T. & Palm, E. (1975), Stability of linear flows Phys. Fluids 18, pp. 487 – 488

    Article  MATH  Google Scholar 

  • Fjørtoft, R. (1950), Application of integral theorems in deriving criteria of stability for laminar flows and for the baroclinic circular vartex17, 6, 52 pp

    Google Scholar 

  • Gustavsson, L. H. (1981), Energy growth of three-dimensional disturbances in plane Poiseuille flowJ. Fluid Mech 224, pp. 243 – 51

    Google Scholar 

  • Landahl, M. T. (1980), A note on algebraic instability of inviscid parallel shear flowsJ Fluid Mech 98, pp. 241 – 60

    Article  MathSciNet  Google Scholar 

  • Landahl, M. T. (1990), On sublayer streaksJ. Fluid Mech 212, pp. 593 – 614.

    Article  MATH  Google Scholar 

  • Landahl, M. T. (1993), Model for the wall-layer structure of a turbulent shear flowEuropean J. Mechanics, B/Fluids 12, pp. 85 – 96

    MATH  Google Scholar 

  • Rayleigh, Lord (1880), On the stability, or instability, of certain fluid motionsProc London Math. Society 11, pp. 57 – 70

    Article  MATH  Google Scholar 

  • Russell, J. M. & Landahl, M. T. (1984), The evolution of a flat eddy near a wall in an inviscid shear flowPhys. Fluids 27, pp. 557 – 70

    Article  MATH  Google Scholar 

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© 1996 Kluwer Academic Publishers

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Landahl, M.T. (1996). Role of Non-Wave-Like Disturbances in Transition. In: Grue, J., Gjevik, B., Weber, J.E. (eds) Waves and Nonlinear Processes in Hydrodynamics. Fluid Mechanics and Its Applications, vol 34. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0253-4_20

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  • DOI: https://doi.org/10.1007/978-94-009-0253-4_20

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6597-9

  • Online ISBN: 978-94-009-0253-4

  • eBook Packages: Springer Book Archive

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