Asymptotic Analysis of a Turbulent Boundary Layer in a Strong Adverse Pressure Gradient

摘要

The structure of an incompressible turbulent boundary layer subjected to a strong adverse pressure gradient is studied by means of an asymptotic analysis of the Reynolds time-averaged equations. Limit-process expansions developed in the limit of large Reynolds number reveal a relatively thick nondefect layer in the outer region of the boundary layer near the exterior inviscid flow, and a relatively thin layer near the wall. To leading orders of approximation, the momentum balance involves convection, pressure gradient, and turbulent stress in the outer layer, and pressure gradient, and turbulent and viscous stresses in the inner layer. The asymptotic expansions for these two layers are matched in an arbitrary intermediate region, wherein the streamwise velocity has a square-root dependence and the Reynolds stress has a corresponding linear dependence on the normal coordinate. The leading-order approximations for the outer and inner layers give rise to similarity formulations, from which appropriate similarity formulations for the distinguished intermediate layer have been identified and developed. These latter formulations are employed to analyze available experimental data.