On wall-bounded turbulent shear flows

Several turbulent wall-bounded flows are investigated by means of similarity analysis, the Asymptotic Invariance Principle and Near-Asymptotics. The flows include pipe and channel flows, plane wall jets, thermal boundary layers and zero pressure gradient boundary layers. Inner and outer regions of these flows can be matched at finite Reynolds number, but become asymptotically independent of it, and reduce to similarity solutions of the inner and outer boundary layer equations in the limit.; A new theory for pipe and channel flow is developed, where Reynolds number dependent logarithmic overlap profiles and a logarithmic friction law provide an excellent description of experimental velocity and skin friction data over more than three and a half decades in Reynolds number. Since the overlap velocity profile is a logarithm in y + a, logarithmic; behavior inside y+ ≈ 300 cannot be established unless the mesolayer and a+ are explicitly accounted for.; A new theory is proposed for the plane wall jet, leading to new scaling parameters, i.e. the Reynolds shear stress in the outer layer scales to first order with $u2*$, so that the outer layer is governed by two velocity scales, U_m and u_*. Velocity profiles in the overlap region and the friction law exhibit power law behavior, with coefficients which depend on local Reynolds number. New scaling laws for the turbulence quantities are derived from the Reynolds stress equations. Excellent agreement with all the experimental data is achieved. The hypothesis that the inner flow of all wall-bounded turbulent flows is the same appears to be supported.; The similarity analysis of George & Castillo (1997) for the isothermal zero pressure-gradient turbulent boundary layer on a flat plate is extended to the thermal boundary layer of forced convection. A new outer temperature scaling is derived. Temperature profiles in the overlap region and the heat transfer law are also power laws. New developments are reported for the zero pressure gradient boundary layer originally treated by George/Castillo. The scaling of Zagarola & Smits (1998) is found to be consistent with the fundamental scaling laws, and it is derived from a separability hypothesis. It is suggested that δ_*/δ is independent of local Reynolds number and uniquely determined by the initial/upstream conditions. A higher order solution for the boundary layer parameters is derived, and tools to distinguish between the classical log-law and the George/Castillo theory are explored.