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High Frequency Rayleigh Instability of Stokes Layers

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Stability of Time Dependent and Spatially Varying Flows

Part of the book series: ICASE NASA LaRC Series ((ICASE/NASA))

Abstract

A knowledge of the conditions under which unsteady flows become turbulent is important in many applications, e.g. the transport of sediment along the ocean bed (Li 1954), physiological investigations of the larger blood vessels (e.g. Pedley 1980), and various pipe-line and aerodynamic problems.

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References

  • Allmen, M.J. & Eagles, P.M. (1984) Stability of divergent channel flows: a numerical approach. Proc. R. Soc. Lond. A392, 359–372.

    ADS  Google Scholar 

  • Benney, D.J. & Rosenblat, S. (1964) Stability of spatially varying and time dependent flows. Phys. Fluids 7, 1385–1386.

    Article  ADS  Google Scholar 

  • Bodonyi, R.J. & Smith, F.T. (1981) The upper branch stability of the Blasius boundary layer, including non-parallel flow effects. Proc. R. Soc. Lond. A375, 65–92.

    MathSciNet  ADS  Google Scholar 

  • Bouthier, M. (1973) Stabilite lineaire des ecoulements presque paralleles. J. de Mecanique 11, 599–621.

    MATH  Google Scholar 

  • Clamen, M. & Minton, P. (1977) An experimental investigation of flow in an oscillating pipe. J. Fluid. Mech. 81, 421–431.

    Article  ADS  Google Scholar 

  • Clarion, C. & Pelissier, R. (1975) A theoretical and experimental study of the velocity distribution and transition to turbulence in free oscillatory flow. J. Fluid Mech. 70, 59–79.

    Article  ADS  MATH  Google Scholar 

  • Collins, J.I. (1963) Inception of turbulence at the bed under periodic gravity waves. J. Geophysical Res. 18, 6007–6014.

    Article  ADS  Google Scholar 

  • Cowley, S.J., Hocking, L.H. and Tutty, O.R. (1985) On the stability of solutions of the classical unsteady boundary-layer equation. Phys. Fluids 28, 441–443.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Davis, S.H. & Rosenblat, S. (1977) On bifurcating periodic solutions at low frequency. Stud. Appl. Math. 57, 59–76.

    MathSciNet  ADS  Google Scholar 

  • Drazin, P.G. & Howard, L.N. (1962) The instability to long waves of unbounded parallel inviscid flow. J. Fluid Mech., 14, 257–283.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Drazin, P.G. & Reid, W.H. (1981) Hydrodynamic Stability. Cambridge University Press.

    MATH  Google Scholar 

  • Finucane, R.G. & Kelly, R.E. (1976) Onset of instability in a fluid layer heated sinusoidally from below. Int. J. Heat Mass Transfer 19, 71–85.

    Article  ADS  MATH  Google Scholar 

  • Gill, A.E. & Davey, A. (1969) Instabilities of a buoyancy-driven system. J. Fluid Mech. 35, 775–798.

    Article  ADS  MATH  Google Scholar 

  • Hall, P. (1978) The linear stability of flat Stokes layers. Proc. R. Soc. Lond. A359, 151–166.

    Article  ADS  Google Scholar 

  • Hall, P. (1983) On the nonlinear stability of slowly varying time-dependent viscous flows. J. Fluid Mech, 126, 357–368.

    Article  ADS  MATH  Google Scholar 

  • Hino, M., Sawamoto, M. & Takasu, S. (1976) Experiments on transition to turbulence in an oscillatory pipe flow. J. Fluid Mech. 75, 193–207.

    Article  ADS  Google Scholar 

  • Howard, L.N. (1964) The number of unstable modes in hydrodynamic stability problems. J. de Mecanique 3, 433–443.

    Google Scholar 

  • Iguchi, M., Ohmi, M. & Megawa, K. (1982) Analysis of free oscillating flow in a U-shaped tube. Bull. JSME 25, 1398–1405.

    Article  Google Scholar 

  • Kiser, K.M., Falsetti, H.L., Yu, K.H., Resitarits, M.R., Francis, G.P. & Carroll, R.J. (1976) Measurements of velocity wave forms in the dog aorta. J. Fluids. Engng. 6, 297–304.

    Article  Google Scholar 

  • Li, H. (1954) Stability of oscillatory laminar flow along a wall. Beach Erosion Board, US Army Corps Eng., Washington, D.C. Tech. Memo No. 47.

    Google Scholar 

  • Lyne, W.H. (1971) Unsteady viscous flow in a curved pipe. J. Fluid Mech. 43, 13–31.

    Article  ADS  Google Scholar 

  • Merkli, P. & Thomann, H. (1975) Transition to turbulence in oscillating pipe flow. J. Fluid Mech. 68, 567–575.

    Article  ADS  Google Scholar 

  • Monkewitz, M. (1983) Ph.D. Thesis No. 7297, Federal Institute of Technology, Zurich, Switzerland.

    Google Scholar 

  • Monkewitz, P.A. & Bunster, A. (1985) The stability of the Stokes layer: visual observations and some theoretical considerations. This volume

    Google Scholar 

  • Nerem, R., Seed, W.A. & Wood, N.B. (1972) An experimental study of the velocity distribution and transition to turbulence in the aorta. J. Fluid Mech. 52, 137–160.

    Article  ADS  Google Scholar 

  • Obremski, H.J. & Morkovin, M.V. (1969) Application of a quasi-steady stability model to periodic boundary-layer flow. AIAA J. 7, 1298–1301.

    Article  ADS  Google Scholar 

  • Ohmi, M., Iguchi, M., Kakehashi, K. & Masuda, T. (1982a) Transition to turbulence and velocity distribution in an oscillating pipe flow. Bull. JSME 25, 365–371.

    Article  Google Scholar 

  • Ohmi, M., Iguchi, M. & Urahata, I. (1982b) Transition to turbulence in a pulsatile pipe flow, part 1, wave forms and distribution of pulsatile velocities near transition region. Bull. JSME 25, 182–189.

    Article  Google Scholar 

  • Pedley, T.J. (1980) The fluid mechanics of large blood vessels. Cambridge University Press.

    Book  MATH  Google Scholar 

  • Pelissier, R. (1979) Stability of a pseudo-periodic flow. J. Appl. Math. Phys. (ZAMP) 30, 577–585.

    Article  MathSciNet  MATH  Google Scholar 

  • Ramaprian, B.R. & Mueller, A. (1980) Transitional periodic boundary layer study. J. Hydr. Div. ASCE W 106, 1959–1971.

    Google Scholar 

  • Riley, N. (1965) Oscillating viscous flows. Mathematika 12, 161–175.

    Article  MathSciNet  Google Scholar 

  • Rosenblat, S. & Herbert, D.M. (1970) Low-frequency modulation of thermal instability. J. Fluid Mech. 43, 385–398.

    Article  ADS  MATH  Google Scholar 

  • Rosenblat, S. (1968) Centrifugal instability of time-dependent flows. Part 1. Inviscid, periodic flows. J. Fluid Mech. 33, 321–336.

    Article  ADS  MATH  Google Scholar 

  • Seminara, G. & Hall, P. (1976) Centrifugal instability of a Stokes layer: linear theory. Proc. R. Soc. Lond. A350, 299–316.

    ADS  Google Scholar 

  • Sergeey, S.I. (1966) Fluid oscillations in pipes at moderate Reynolds numbers. Mekh. Zhidk. Gaza. 1, 168–170 (Transl. in Fluid Dyn. 1, 121–122).

    Google Scholar 

  • Smith, F.T. (1979) On the non-parallel flow stability of the Blasius boundary layer. Proc. Roy. Soc. Lond. A336, 91–109.

    ADS  Google Scholar 

  • Tollmien, W. (1936) General instability criterion of laminar velocity distributions. Tech. Memor. Nat. Adv. Comm. Aero. Wash. No. 792.

    Google Scholar 

  • Tromans, P. (1977) Ph.D Thesis, University of Cambridge.

    Google Scholar 

  • Tutty, O.R. & Cowley, S.J. (1985) On the stability and the numerical solution of the unsteady interactive boundary-layer equation. Submitted to J. Fluid Mech.

    Google Scholar 

  • von Kerczek, C. (1973) Ph.D. Thesis, The Johns Hopkins University.

    Google Scholar 

  • von Kerczek, C. (1982) The instability of oscillatory pi ane Poiseuille flow. J. Fluid Mech. 116, 91–114.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • von Kerczek, C. & Davis, S.H. (1974) Linear stability theory of oscillatory Stokes layers, J. Fluid Mech. 62, 753–773.

    Article  ADS  MATH  Google Scholar 

  • von Kerczek, C. & Davis, S.H. (1976) The instability of a stratified periodic boundary layer. J. Fluid Mech. 75 287–303.

    Article  ADS  MATH  Google Scholar 

  • Yang, W.H. & Yih, C.-S. (1977) Stability of time-periodic flows in a circular pipe. J. Fluid Mech. 82, 497–505.

    Article  ADS  MATH  Google Scholar 

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Authors
  1. Stephen J. Cowley
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Editor information

Editors and Affiliations

  1. NASA Langley Research Center, 23665, Hampton, VA, USA

    D. L. Dwoyer

  2. NASA Langley Research Center, Institute for Computer Applications in Science and Engineering (ICASE), ICASE/NASA, 23665, Hampton, VA, USA

    M. Y. Hussaini

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© 1987 Springer-Verlag New York Inc.

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Cowley, S.J. (1987). High Frequency Rayleigh Instability of Stokes Layers. In: Dwoyer, D.L., Hussaini, M.Y. (eds) Stability of Time Dependent and Spatially Varying Flows. ICASE NASA LaRC Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4724-1_14

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  • DOI: https://doi.org/10.1007/978-1-4612-4724-1_14

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96472-0

  • Online ISBN: 978-1-4612-4724-1

  • eBook Packages: Springer Book Archive

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