Nomenclature a = speed of sound C = normalized density-viscosity product, C p = pressure coefficient, 2(p -p x )/p x Ul, c = chord length c fx = local skin friction coefficient for circumferential flow, 2(/jLdu/dz) w /p e ul f = transformed circumferential component of vector potential, i^(0, r, z)/(2£r/r 0 ) 1/2 G = transformed radial component of vector potential (alternative), (v e /q e )g g = transformed radial component of vector potential, w> 2 (0, r, z)/r(2gr/r 0 ) l/2 v e H = total enthalpy M x = Mach number of undisturbed stream, UJa p = static pressure q e = resultant external velocity, r = radial distance along generator, measured from cone apex, O r () = radius of sphere centered at O, intersecting leading edge of streamwise section S = enthalpy parameter, HIH e -1 T = static temperature U x = velocity of undisturbed stream (w, v, w) = velocity components in (0, r, z) directions v = spanwise velocity, -v x = arc distance around surface, r 0 0 y = spanwise distance, r () -r z = distance normal to surface y = ratio of principal specific heat capacities of gas A = transformed boundary-layer thickness 8 * = displacement thickness of circumferential flow, S'o (1 -pulp e u e ) dz 77 = similarity variable used in present work, u e /f, p dz/V2fr/r 0 VK-C = similarity variable used by Kaups and Cebeci, Vv e /p e /z e r 0 Jg p dz 0 = polar angle in developed plane, measured from stagnation line A H A 2 = sweep angles of leading and trailing edges fji = coefficient of viscosity of gas f = transformed circumferential coordinate, So Pet*> e u e r () d0 p = mass density of gas o-= Prandtl number of gas

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SummaryMeasurements are presented of the mean flow properties of some three-dimensional turbulent boundary layers re-developing after reattachment behind short separation bubbles yawed at 26.5° to the main stream. For these measurements, Rθ11varied from about 550 to 1450. It was found that, where the pressure gradient parameter (ν/ρu3τ1)∂p/∂s was not greater than about 0.05, the flow in the local external streamline direction conformed well with empirical laws for fully-attached two-dimensional layers with regard to the mean velocity profiles, shape parameter relationships and skin friction laws, giving support to the usual assumption that these two-dimensional relationships may be applied to the streamwise flow in three-dimensional layers, subject to the limitation on the pressure gradient parameter. The cross-flow profiles, on the other hand, were not generally fitted well by the often-used representations of Mager and Johnston. The variations of the kinetic energy dissipation coefficient and the entrainment rate were deduced for one of the layers, both quantities being found to be higher than those predicted by empirical relationships for conventionally-developing two-dimensional layers. However, the energy dissipation is in fair agreement with that in a similarly re-developing two-dimensional flow.

Abstract. In this paper, we examine the acoustic receptivity of a laminar boundary layer with an isolated 3-D surface roughness. Stimulus-response experiments are conducted to quantify the coupling between artificial acoustic excitation and Tollmein-Schlichting instabilities in a Blasius boundary layer. Sophisticated signal processing is used to decompose phase-averaged measurements of the streamwise fluctuating velocity. A retractable roughness element was developed specifically to assist in the measurement of the small disturbance amplitudes encountered. Measurements reveal the existence of a characteristic heart-shaped distur,bance wedge downstream from the roughness. This behaviour is consistent with the numerical and asymptotic work of other authors, who also predict the off-centreline peak amplitude that is observed several wavelengths downstream from the roughness.

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