1. Turbulence 1: Turbulent Boundary layer
By Dana Elam

2. What is Turbulence?
Laminar - flow is steady and constant in position and time
Turbulent - the fluid velocity field varies significantly and irregularly

3. Laminar -Turbulence Transition
In 1883, Prof. Osborne Reynolds produced the first study on transition of laminar flow to turbulent flow
Using:
Where U is area-averaged velocity
L is the pipe diameter
Laminar <2300, fully turbulent > 4000

4. Laminar to Turbulence transition

5. Is Turbulence desired or not?
Depends on the engineering application

6. Why is Turbulence Study Important?
Major reasons are that:
Vast majority of flows are turbulent
Mixing of matter, momentum and heat is of great importance, turbulence increases these processes.
For instance the mixing of momentum of a fluid and as a consequence the wall shear stress and hence skin friction is much greater than if the flow was laminar

7. Turbulent Boundary Layers

8. Turbulent Structures within the Boundary Layer
Since the 60’s research has been made on turbulent structures on wall bounded flows
The aim being to:
Seek order within apparent chaos
Explain patterns in flow visualization, with the aim of modifying them.

9. Turbulent wall flows
The turbulent boundary layer ; ‘That part of the flow into which the vorticity originally generated at the surface has now spread’
Fluctuating motion outside layer not called turbulent.

10. Structures found in wall flows:
Low-speed streaks
Ejections of low-speed fluid outward from the wall
Sweeps of high-speed fluid toward the fall
Vortical structures of several proposed forms
Strong internal shear layers in the wall zone
Near wall pockets, observed as areas clear of marked fluid
Backs: surfaces across which the streamwise velocity changes abruptly
Large scale motions in the outer layers (superlayers and deep valleys of free stream fluid) [Kline and Robinson, 1990]

11. Hairpin Vortices Vortex field of vortex filaments
Stream-wise fluctuation sweep put axial component
Vortex loop gets stretched out by higher mean velocity

12. Low-Speed Streaks Streaks exist in the near-wall region y+<40
Streaks about 80 to 120v apart, up to 1,000v long

13. Ejection & Sweep
Streaks burst, they move slowly away from the wall, at y+ ≈10, moves away more rapidly from the wall, Ejection
Ejection causes corresponding sweep

14. Viscous Super-layer
The larger structures seen, can be composed of an ensemble of smaller structures
Valleys of non-turbulent fluid that penetrate deep into boundary layer
Valleys separate large eddies or bulges
A viscous super-layer separates the turbulent boundary layer

16. Wall Units

17. Channel Flow
For a duct where h = 2, L/ >>1, w/>>1

18. 
From the reynolds equation:

19. Where the total shear stress:

20. Shear Stress
At the wall, U(x,t)=0 dictates that all the Reynolds stresses are zero, and only viscous stress is a factor

21. Co-efficent of Friction

22. Friction Velocity

23. Wall Units
Viscosity and wall shear stress are important parameters and non-dimensionalized units can be derived
Viscous Lengthscale:

24. Wall Units 2
Friction Reynolds Number:
Wall Units: