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The turbulent energy equation is converted into a differential equation for the turbulent shear stress by defining three empirical functions relating the turbulent intensity, diffusion and dissipation to the shear stress profile. This equation, the mean momentum equation and the mean continuity equation form a hyperbolic system. Numerical integrations by the method of characteristics with preliminary choices of the three empirical functions compare favourably with the results of conventional calculation methods over a wide range of pressure gradients. Nearly all the empirical information required has been derived solely from the boundary layer in zero pressure gradient.
Bradshaw et al. (1967) studied this question.