

Section 12: Basic Concepts in Turbulence Modeling  
12.1  Comments on laminar flow, its stability, and the transition to turbulent flow.  
12.2  Features of turbulent flows (high Reynolds number, "randomness", three dimensionality of fluctuations, intermittency near free boundaries, role of viscous dissipation, etc.).  
12.3  The range of scales in turbulent motion; the Kolmogorov microscale. Limitations imposed by computer memory and speed on attempts to obtain exact numerical solutions (fluctuations and all!) of the NavierStokes equations for turbulent, high Reynolds number flows.  
12.4  Statistical averages of random quantities in turbulent flow. Reynolds' equation for the mean flow; the Reynolds stress and the closure problem.  
12.5  Prandtl's mixing length hypothesis: a simple "mean flow" (or "zeroequation") closure model.  
12.6  Prandtl's closure hypothesis for free turbulent flows (jets, wakes). A rough backoftheenvelope "solution" for a round turbulent jet.  
12.7  The nature of wallbounded turbulent flows: the outer and inner layers, the "universal law of the wall" for the inner layer; the logarithmic sublayer and the viscous sublayer. Derivation of the logarithmic meanvelocity profile from Prandtl's mixing length model.  
Reading  
General References: Sonin, A. S., & Yaglom, A. M., Statistical Fluid Mechanics, Vol. 1, MIT (see Chapter 3 in particular) Schlichting, H., Boundary Layer Theory (7th edition), McGrawHill Tritton, D. J., Physical Fluid Dynamics (2nd edition), Oxford White, Frank M., Viscous Fluid Flow, 2nd edition, McGrawHill 
