An analysis is made of the unsteady lift exerted on a stationary rigid body
immersed in an incompressible, plane-wall turbulent boundary layer. The li
ft is expressed as a surface integral over the body involving the upwash ve
locity induced by the "free" vorticity Omega (found by taking explicit acco
unt of the interaction of the body with the flow and excluding the bound vo
rticity) and a harmonic function X-2 that depends only on the shape of the
body. The upwash velocity is the free-field velocity given in terms of Omeg
a by the Biot-Savart formula, augmented by the velocity field of a conventi
onal distribution of image vortices in the wall. The function X-2 can be in
terpreted as the velocity potential of flow past the body, produced by moti
on of the wall at unit speed towards the body. Detailed predictions are mad
e of the lift on a slender airfoil placed in the outer region of the bounda
ry-layer. When the airfoil chord is large compared to the boundary-layer th
ickness, vortex shedding into the wake causes the magnitude of the net upwa
sh velocity near the trailing edge to be small. The main contributions to t
he surface integral are then from the nose region, where the upwash velocit
y may be estimated independently of the fluctuations near the trailing edge
. Analytical results for a thin plate airfoil of chord 2a at distance h fro
m the wall show that the lift increases as alh increases; it is ultimately
independent of a and scales with the ratio of h to the hydrodynamic wavelen
gth. Application is made to determine the sound generated by the airfoil in
a weakly compressible boundary layer flow over a finite elastic plate. (C)
2001 Academic Press.