Memory effect in a turbulent boundary-layer flow due to a relatively strong axial variation of the mean-velocity gradient

Abstract

Measurements have been made of the distributions of mean velocity, turbulence intensities and turbulence shear-stress in a turbulent boundary-layer downstream of a hemi-spherical cap attached onto the plane rigid wall. The eddy-viscosity, when computed in the classical way according to Boussinesq's concept from the lateral gradient of the mean velocity and the turbulence shear-stress, showed a very strong non-uniform lateral distribution, also across the outer region of the boundary-layer. Moreover, the non-dimensional values of the eddy-viscosity, using the wall-friction velocity and the boundary-layer thickness as the velocity scale and length scale respectively, were higher than those for the boundary-layer when not disturbed by the wake of the spherical cap.

However, when account is taken of an axial memory effect of the stream-wise variation of the lateral gradient of the mean-velocity, the values of the non-dimensional eddy viscosity are close to those for the undisturbed boundary-layer.