Threshold Conditions for Breakdown of Laminar Boundary Layers

  • Thorwald Herbert
  • Jeffrey D. Crouch
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

Summary

A perturbation method based on a simultaneous expansion for primary and secondary modes of instability is used to study the flow field in the later stages of transition. Results of the analysis are in good agreement with experimental data for amplitudes in excess of 5% that cause immediate breakdown. Threshold conditions for sustained growth of subharmonic modes past branch II are calculated. These conditions are presented both in terms of branch II amplitudes and initial amplitudes.

Keywords

Borate 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. T. C. Corke and R. A. Mangano (1987) “Transition of a boundary layer: controlled fundamental-subharmonic interactions,” Fluid Dynamics Center Rep. No. 87–1, Illinois Institute of Technology, Chicago, IllinoisGoogle Scholar
  2. K. C. Cornelius (1985) “Three dimensional wave development during boundary layer transition,” Lockheed Georgia Res. Rep. LG85RR0004, Marietta, Georgia..Google Scholar
  3. J. D. Crouch (1988) “The nonlinear evolution of secondary instabilities in boundary layers,” VPI & SU, Ph.D. thesis..Google Scholar
  4. J. D. Crouch and Th. Herbert (1986) “Perturbation analysis of nonlinear secondary instabilities in boundary layers,” Bull. Am. Phys. Soc., Vol. 31, pp. 1718.Google Scholar
  5. Th. Herbert (1988) “Secondary instability of boundary layers,” Ann. Rev. Fluid Mech., Vol. 20, pp. 487–526.ADSCrossRefGoogle Scholar
  6. Yu. S. Kachanov, V. V. Kozlov, and V. Ya. Levchenko (1977) “Nonlinear development of a wave in a boundary layer,” Izv. AN USSR, Mekh. Zhidk. i Gaza,Vol. 3, pp. 49–53. (In Russian)Google Scholar
  7. Yu. S. Kachanov and V. Ya. Levchenko (1984) “The resonant interaction of disturbances at laminar-turbulent transition in a boundary layer,” J. Fluid Mech., Vol. 138, pp. 209–247.ADSCrossRefGoogle Scholar
  8. P. S. Kiebanoff, K. D. Tidstrom, and L. M. Sargent (1962) “The three-dimensional nature of boundary-layer instability,” J. Fluid Mech., Vol. 12, pp. 1–34.ADSCrossRefGoogle Scholar
  9. P. R. Spalart, and K.-S. Yang (1987) “Numerical study of ribbon-induced transition in Blasius Flow,” J. Fluid Mech., Vol. 178, pp. 345–365ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Thorwald Herbert
    • 1
  • Jeffrey D. Crouch
    • 2
  1. 1.Department of Mechanical Engineering Department of Aeronautical and Astronautical EngineeringThe Ohio State UniversityColumbusUSA
  2. 2.Laboratory for Computational Physics and Fluid DynamicsNaval Research Laboratory, Code 4420USA

Personalised recommendations