Asymptotic theory for turbulent shear flows at high Reynolds numbers

It is shown that a complete asymptotic theory of turbulent shear flows at h igh Reynolds numbers near walls exists for the following three standard cla sses of flows: attached boundary layers, Stratford flows (tau (w) = 0) and natural convection flows. These flows are characterized by a finite thickne ss and a layer structure. The Reynolds-averaged Navier-Stokes equations tog ether with an appropriate turbulence model can be solved by the method of m atched asymptotic expansions. Hereby the matching conditions between the di fferent layers yield boundary conditions for the solutions of the equations of motion and furthermore conditions, which asymptotically correct turbule nce models have to satisfy. As typical results of the asymptotic theory gen eral explicit formulae for the distributions of the shear stress and the he at flux at the M,all exist (usually power laws except the logarithmic laws for attached boundary layers). For more general classes of flow, e.g. bound ary layers with separation, combined natural and forced convections, a comp lete asymptotic theory is not yet available, because their solutions depend on additional coupling parameters that contain the viscosity.