The matching problem in the theory of nonequilibrium turbulent flows near a wall

Analysis of the available data on strongly nonequilibrium turbulent wall flows indicates the difficulties arising in their calculation. One of the reasons for these difficulties is the "local" nature of the semiempirical theories of turbulence. Another relates to the way in which the solutions in the inner and outer regions are matched. It is shown that the traditional method of matching the solutions on the basis of the local values of the coefficients of turbulent viscosity in the inner region, where the "wall law" holds, and the outer region, where the "wake law" holds, results in an incorrect determination of the scale of the inner region and is therefore incorrect. Integral matching based on the tangential turbulent stresses is considered. Concrete calculations in the framework of a two-parameter integral method show that integral matching leads to a qualitatively correct description of the dynamic interaction between the inner and outer regions. The results of calculations of the integral characteristics of a turbulent boundary layer are compared with experimental data.