Self-similar flows in a turbulent boundary layer, when the free-stream velocity is specified as a power function of the longitudinal coordinate, are investigated. The self-similar formulation not only simplifies solving the problem by reducing the equations of motion to ordinary differential equations but also provides a means for formulating closure conditions for the problem. It is shown that, for the class of flows under consideration that depend on three governing parameters, the dimensionless mixing length is a function of the normalized distance from the wall and the exponent m in the outer region, and a universal function of the local Reynolds number in the wall region, the latter corollary being true even when the skin friction vanishes. In calculations, this function is set to be independent of the pressure gradient, which gives the results very close to experimental data. There exist four different self-similar flow regimes. Each regime is related to its similarity parameter, one of which is the well-known Clauser equilibrium parameter and the other three are established for the first time. In case of the adverse pressure gradient when the exponent lies within certain limits, which depend on Reynolds number, the problem has two solutions with different values of the boundary layer thickness and skin friction, which points out the possibility of hysteresis in the near-separating flow. Separation occurs not at the minimal value of m that corresponds to the strongest adverse pressure gradient but at a higher one, whose dependence on Reynolds number is calculated in the paper. The results of the theory are in good agreement with experimental data.
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