SCALING OF ADVERSE-PRESSURE-GRADIENT TURBULENT BOUNDARY-LAYERS

An asymptotic analysis is developed for turbulent boundary layers in strong adverse pressure gradients. It is found that the boundary layer divides into three distinguishable regions: these are the wall layer, the wake layer and a transition layer. This structure has two key differences from the zero-pressure-gradient boundary layer: the wall layer is not exponentially thinner than the wake; and the wake has a large velocity deficit, and cannot be linearized. The mean velocity profile has a y1/2 behaviour in the overlap layer between the wall and transition regions. The analysis is done in the context of eddy viscosity closure modelling. It is found that k-epsilon-type models are suitable to the wall region, and have a power-law solution in the y1/2 layer. The outer-region scaling precludes the usual epsilon-equation. The Clauser, constant-viscosity model is used in that region. An asymptotic expansion of the mean flow and matching between the three regions is carried out in order to determine the relation between skin friction and pressure gradient. Numerical calculations are done for self-similar flow. It is found that the surface shear stress is a double-valued function of the pressure gradient in a small range of pressure gradients.