AN ASYMPTOTIC DESCRIPTION OF THE ATTACHED, TURBULENT, OSCILLATORY BOUNDARY-LAYER

The attached, temporally-oscillating turbulent boundary layer is inves tigated by use of asymptotic matching techniques, valid for the limit of large Reynolds numbers, Much of the analysis is applicable to gener ally accepted turbulence models (which satisfy a few basic assumptions as detailed in the paper), and this is then applied in particular to two well established turbulence models, namely the k - epsilon transpo rt model and the Baldwin-Lomax mixing-length model. As in the laminar case, the steady-streaming Reynolds number is found to be an important parameter, although in the turbulent case this is important at leadin g (rather than second) order. In particular, the time dependence of th e wall shear land the displacement thickness) is found to leading orde r to be independent of the specific closure model, but just differs by a multiplicative constant dependent on the particular model. Results are also compared with previous computational and experimental data; t he agreement is encouraging. In addition to describing the oscillatory flow above a flat wall, these leading order results an applicable to flow past general bodies, provided the amplitude of oscillation is sma ll compared to the surface radius of curvature. In the case of the Bal dwin-Lomax model, the nature of the higher-order terms, including the steady streaming caused by the interaction of curvature and inertia ef fects is also investigated. This analysis suggests some limitations on the applicability of the model to the finer details of the flow, due to the occurrence of discontinuities land singularities) in the higher -order asymptotic solution, particularly when inertia effects are take n into account.