TY - JOUR

T1 - Analysis of the unstable Tollmien-Schlichting mode on bodies with a rounded leading edge using the parabolized stability equation

AU - Turner, M.R.

AU - Hammerton, P.W.

N1 - © The Author(s) and Cambridge University Press, 2009

PY - 2009

Y1 - 2009

N2 - 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
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.

AB - 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
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.

U2 - 10.1017/S0022112008005260

DO - 10.1017/S0022112008005260

M3 - Article

VL - 623

SP - 167

EP - 185

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -