Prandtl’s mixing length model

Application of the Governing Equations to Turbulent Flow 123 Prandtl s Mixing-Length Model... 

Supported by experimental observations, v y is assumed to be of the same order of magnitude as v in the constant stress layer near a solid boundary. Hence, we may define Prandtl s mixing length model as ... 

Another method of trying to describe the turbulence terms in the above equations is by means of Prandtl s mixing length theory. The mixing length concept will be introduced in this section and some simple turbulence models based on this concept will be discussed [1],[2],[3],[6],[7]. 

For power law fluids, Tomlta (1959) extended his laminar flow model (discussed in Section 5.2.1.3) to turbulent flows in smooth pipes by applying Prandtl s mixing length concept, and developed a different implicit equation ... 

Prandtl s model derivation can then be briefly sketched, introducing the Boussinesq [19] [20] approximation for the turbulent viscosity. Starting out with the simple kinetic theory relation that the molecular viscosity equals the molecular velocity times the mean free path, an analogous relation can be formulated for the turbulent viscosity in terms of the turbulent mixing length and a suitable velocity scale, Ut Iv. ... 

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