1. WALL FREE SHEAR FLOW Turbulent flows free of solid boundaries JET Two-dimensional image of an axisymmetric water jet, obtained by the laser-induced fluorescence technique. (From R. R. Prasad and K. R. Sreenivasan, Measurement and interpretation of fractal dimension of the scalar interface in turbulent flows, Phys. Fluids A, 2:792–807, 1990) x y Irrotational Turbulent

2. WAKE http://www.ifh.uni-karlsruhe.de/science/envflu/

3. SHEAR LAYER

4. Laser-Induced Fluorescence (LIF) VISUALIZATION OF AN AXISYMMETRIC TURBULENT JET, C. Fukushima and J. Westerweel, Technical University of Delft, The Netherlands x

5. x Turbulent Kinetic Energy (q 2 ) Balance in a Jet

6. x y q2q2 - y m 2 /s 2

7. Laser-Induced Fluorescence (LIF) VISUALIZATION OF AN AXISYMMETRIC TURBULENT JET, C. Fukushima and J. Westerweel, Technical University of Delft, The Netherlands x Turbulent Kinetic Energy (q 2 ) Balance in a Jet No local accelerations No viscous transport Part of the shear production = 0 No buoyancy production

8. x y y m 2 /s 3 Gain Loss

9. http://www.symscape.com/node/447 U0U0 WALL-BOUNDED SHEAR FLOW Nominal limit of boundary layer 0.99U 0 Viscous sublayer For fully developed, bounded turbulent flow (not changing in x):

10. Function of x only Function of z only CONSTANTS! z centerline or surface

11. in boundary layer: zz edge of boundary layer stress is a function of x and z

12. Near the wall – Different Layers http://furtech.typepad.com/ z ū (x) u(x,z) Onlyinvolve mass dimension Should appear together in nondimensional groups Friction Velocity

13. This relates 4 variables involving the dimensions of length and time According to the PI THEOREM, this relationship has 4 variables and 2 dimensions Then, only two (4 – 2) non-dimensional groups can result: Law of the Wall Inner part of the wall layer, right next to the wall, is called the viscous sublayer – dominated by viscous effects

14. z (m) = z + ν/u * viscous sublayer buffer layer logarithmic layer

15. viscous sublayer buffer layer logarithmic layer outer layer Velocity defect law Law of the wall Karman constant = 0.41 Equating and multiplying times z/u *

16. Karman constant = 0.41 Integrating: From experiments: Velocity distributions for the Overlap layer, Inertial sublayer, Logarithmic layer Logarithmic velocity distribution near a boundary can also be derived from dimensional analysis

17. can only depend on z, and the only relevant velocity scale is u *

18. Data from Ponce de Leon Inlet Florida Intracoastal Waterway Florida