Analysis of a turbulent boundary layer subjected to a strong adverse pressure gradient

Abstract

We define two non-dimensional parameters Λ = τ w p xδ and R p = U pδ ν where τ w is the wall stress, p x (⪢0) is the pressure gradient to which the turbulent boundary layer (of thickness δ) is subjected, ν is the kinematic viscosity, U p = ( νp x p ) 1 3 is a characteristic velocity and p is the density. The limit corresponding to the strong adverse pressure gradient is formulated as Λ → 0, R p → ∞, ΛR p finite. Using appropriate inner and outer asympcotic expansions, both above a wall layer possibly scaling with τ w and ν, it is found by an application of Millikan's argument that there is an inertial sublayer where the streamwise velocity distribution obeys a half-power law, whose slope depends on Λ, and intercept on ΛR p . Indeed comparison with available experimental data shows the inner law to be well represented by u Up = (3.5 + 19Λ)( yU p ν ) 1 2 + 2.5ΛR p . The outer flow obeys a generalized defect law; use of constant eddy viscosity closure yields results in good agreement with experiment.