Skip to main content
Article thumbnail
Location of Repository

Analysis of the unstable Tollmien-Schlichting mode on bodies with a rounded leading edge using the parabolized stability equation

By M.R. Turner and P.W. Hammerton


The interaction between free-stream disturbances and the boundary layer on a body with a rounded leading edge is considered in this paper. A method which incorporates\ud calculations using the parabolized stability equation (PSE) in the Orr-Sommerfeld region along with an upstream boundary condition derived from asymptotic theory in the vicinity of the leading edge, is generalised to bodies with an inviscid slip velocity which tends to a constant far downstream. We present results for the position of the lower branch neutral stability point and the magnitude of the unstable Tollmien-Schlichting (T-S) mode at this point for both a parabolic body and the Rankine body. For the Rankine body, which has an adverse pressure gradient along its surface far from the nose, we find a double maximum in the T-S wave amplitude for sufficiently large Reynolds numbers

Topics: G100 Mathematics, H000 Engineering
Publisher: Cambridge University Press
Year: 2009
DOI identifier: 10.1017/S0022112008005260
OAI identifier:

Suggested articles


  1. (2005). Acoustic receptivity of the boundary layer over parabolic bodies at angles of attack. doi
  2. (2007). Analysis of the unstable T–S mode on bodies with a rounded leading edge 19 doi
  3. (2006). Asymptotic receptivity analysis and the Parabolized Stability Equation : a combined approach to boundary layer transition. doi
  4. (2001). Boundary Layer Receptivity of a Flat Plate with a Rounded Leading Edge. doi
  5. (2001). Boundary layer receptivity to free-stream sound on elliptic edges of flat plates. doi
  6. (1998). Boundary layer receptivity to free-stream sound on parabolic bodies. doi
  7. (2001). Boundary layer receptivity to sound at incident angles. doi
  8. (1996). Boundary-layer receptivity for a parabolic leading edge. doi
  9. (2002). Boundary-layer receptivity to freestream disturbances. doi
  10. (1989). Boundary-layer receptivity to long-wave freestream disturbances. doi
  11. (1999). Comparison of Lam-Rott and Brown-Stewartson eigensolutions of the boundary-layer equations. doi
  12. (1994). Direct numerical simulation of transition: the spatial approach.
  13. (1992). Distortion of a flat-plate boundary layer by free-stream vorticity normal to the plate. doi
  14. (1993). Eigen-functions of linearized unsteady boundary layer equations. doi
  15. (1990). Generation of boundary instability waves by acoustic and vortical freestream disturbances. Laminar-Turbulent Transition, Vol III. doi
  16. (1982). Generation of Tollmien-Schlichting waves by free-stream disturbances at low Mach numbers. doi
  17. (1985). Guide to experiments on instability and laminar-turbulent transition in shear layers.
  18. (1998). Influence of high-amplitude noise on boundary-layer transition to turbulence. doi
  19. (1963). Laminar Boundary Layers. An account of the development, structure and stability of laminar boundary layers in incompressible fluids, together with a description of the associated experimental techniques.
  20. (1992). Linear and nonlinear stability of the Blasius boundary layer. doi
  21. (1975). Nonparallel stability of boundary-layer flows. doi
  22. (2005). Numerical and Asymptotic Approaches to Boundary-Layer Receptivity and Transition.
  23. (1998). On a stabilization procedure for the parabolic stability equations.
  24. (1974). On the effects of boundary-layer growth on flow stability. doi
  25. (1979). On the non-parallel flow stability of the Blasius boundary layer. doi
  26. (1998). On the Practical Application of the PSE Approach to Linear Stability Analysis. doi
  27. (1973). On the propagation of disturbances in a laminar boundary layer. doi
  28. (1993). Parabolized Stability Equations. doi
  29. (1985). Scattering of acoustic waves into Tollmien-Schlichting waves by small streamwise variations in surface geometry. doi
  30. (1963). Some perturbation solutions in laminar boundary-layer theory. Part 1. The momentum equation. doi
  31. (1983). The evolution of Tollmien-Schlichting waves near a leading edge. doi
  32. (2003). The Langley Stability and Transition Analysis Code (LASTRAC): LST, doi
  33. (1960). Theory of linearized time-dependent boundary layers.

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.