1. The Fluid Dynamics of Tornadoes
Richard Rotunno
NCAR
Lecture 4: End-Wall Boundary Layer, Vortex & Corner Flow
NCAR is funded by the National Science Foundation

2. Two-Celled Vortex Outer Flow End-Wall Vortex End-Wall Boundary Layer
Corner Flow

3. Basics of Rotating Boundary-Layer Flow
Richard Rotunno
NCAR, Boulder CO
NCAR is funded by the National Science Foundation

4. Rotating Flow / No Boundary
Simple Vortex

5. 2. Rotating Flow/Frictional Boundary layer

6. 2. Rotating Flow/Frictional Boundary layer
Bathtub Vortex
Dye Injected at
Water Surface
(earlier)
Drain
“Secondary Flow”

7. 2. Rotating Flow/Frictional Boundary layer
Bathtub Vortex
Dye Injected at
Water Surface
(later)
Drain
“Secondary Flow”

8. 2. Rotating Flow/Frictional Boundary layer
Bathtub Vortex
Drain
Dye Injected near
Bottom (earlier)
“Secondary Flow”

9. 2. Rotating Flow/Frictional Boundary layer
Bathtub Vortex
Drain
Dye Injected near
Bottom (later)
“Secondary Flow”

10. 2. Rotating Flow/Frictional Boundary layer

11. 2. Rotating Flow/Frictional Boundary layer
Thought experiment:
Apply lower b.c. at t=0

12. 2. Rotating Flow/Frictional Boundary layer
For any , (radial inflow) near frictional boundary

13. 3. Potential Vortex Above a Stationary Disk: Experiment
Phillips and Khoo (1987, Proc. Roy. Soc. London)

14. 3. Potential Vortex Above a Stationary Disk: Experiment
Phillips and Khoo (1987, Proc. Roy. Soc. London)

15. 3. Potential Vortex Above a Stationary Disk: Theory
radial
tangential
decreasing
radius
decreasing
radius
Burggraf, Stewartson and Belcher (1971, Phys. Fluids)

16. 3. Potential Vortex Above a Stationary Disk: Theory & Experiment
radial
tangential
Phillips and Khoo (1987, Proc. Roy. Soc. London)

17. 3. Potential Vortex Above a Stationary Disk: Theory & Experiment
radial
tangential
Inertial layer:
Friction layer:
Phillips and Khoo (1987, Proc. Roy. Soc. London)
Wilson and Rotunno
(1986, Phys. Fluids)

18. Vortex Breakdown End-Wall Vortex
3. Potential Vortex Above a Stationary Disk: Experiment
Vortex Breakdown
End-Wall Vortex
Phillips (1985, Proc. Roy. Soc. London)

19. Corner Flow, End-Wall Vortex and Boundary layer

20. Simulations
End-Wall Boundary Layer

21. Simulations
Corner Flow ?
End-Wall Boundary Layer

22. Simulations
End-Wall Vortex
Corner Flow ?
End-Wall Boundary Layer

23. Steady, Inviscid, Nondimensional Momentum Equations
Vorticity
Batchelor (1967, An Introduction to Fluid Dynamics, Chap. 7.5)

24. Steady, Inviscid, Nondimensional Momentum Equations
Vorticity
Batchelor (1967, An Introduction to Fluid Dynamics, Chap. 7.5)

25. Example Outflow  Inflow 
Batchelor (1967, An Introduction to Fluid Dynamics, Chap. 7.5)

26. Theory Fiedler&Rotunno (1986, JAS) End-Wall Vortex Corner Flow
End-Wall Boundary Layer of a
Potential Vortex
Rotunno (1980, JFM)
Wilson&Rotunno(1986, Phys. Fluids)
Burggraf et al (1971, Phys. Fluids)

27. Simulations
End-Wall Vortex
Corner Flow
End-Wall Boundary Layer

28. End-Wall Boundary Layer
Outer Flow
End-Wall Boundary Layer

29. End-Wall Vortex Outer Flow End-Wall Vortex End-Wall Boundary Layer
Corner Flow

30. Two-Celled Vortex Outer Flow End-Wall Vortex End-Wall Boundary Layer
Corner Flow

31. Vortex Breakdown
Pauley and Snow (1988, MWR)

32. Summary Boundary Layer of a Potential Vortex 
Boundary Layer of a Potential Vortex  Corner Flow and End-Wall Vortex
Generally Giving a Mismatch Between End-Wall and Two-Celled Vortices