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Basics of Rotating Boundary-Layer Flow

Basics of Rotating Boundary-Layer Flow. Richard Rotunno NCAR, Boulder CO. http:// www.mmm.ucar.edu/people/rotunno /. NCAR is funded by the National Science Foundation. Outline. Rotating Flow / No Boundary Rotating Flow / Frictional Boundary Layer

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Basics of Rotating Boundary-Layer Flow

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  1. Basics of Rotating Boundary-Layer Flow Richard Rotunno NCAR, Boulder CO http://www.mmm.ucar.edu/people/rotunno/ NCAR is funded by the National Science Foundation

  2. Outline • Rotating Flow / No Boundary • Rotating Flow / Frictional Boundary Layer • Boundary Layer of a Solid-Body-Rotation Vortex • Boundary Layer of a Potential Vortex • Boundary Layer of a Rankine-Type Vortex 6. Summary

  3. Rotating Flow / No Boundary Cylindrical Polar Coordinates

  4. Rotating Flow / No Boundary Simple Vortex

  5. 2. Rotating Flow/Frictional Boundary layer http://web.mit.edu/hml/ncfmf.html

  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 For any , (radial inflow) near frictional boundary

  12. 2. Rotating Flow/Frictional Boundary layer Behavior of near frictional boundary depends on Similarity solutions exist Solid-body rotation Potential vortex Rott and Lewellen (1966 Prog Aero Sci)

  13. 3. Flow in Solid-Body Rotation Above a Stationary Disk* * Bödewadt (1940) (Schlichting 1968 Boundary Layer Theory)

  14. 3. Flow in Solid-Body Rotation Above a Stationary Disk Solution exhibits “overshoot” and “pumping”

  15. 3. Flow in Solid-Body Rotation Above a Stationary Disk hodograph Bödewadt Ekman Ekman is linearized version of Bödewadt

  16. 3. Flow in Solid-Body Rotation Above a Stationary Disk 8 0 0 1 -1 0 1 -1 0 1 Inertial layer: Friction layer: Rotunno and Bryan (Submitted to JAS)

  17. 3. Flow in Solid-Body Rotation Above a Stationary Disk Laboratory Experiment radial tangential “Secondary Flow”

  18. 3. Flow in Solid-Body Rotation Above a Stationary Disk Hurricane Inner-Core Flow

  19. 3. Flow in Solid-Body Rotation Above a Stationary Disk Composite Dropsonde Analysis of Hurricane Inner-Core Flow radial tangential Zhang, Rogers, Nolan & Marks (2011, Monthly Weather Review)

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

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

  22. 4. Potential Vortex Above a Stationary Disk: Theory radial tangential decreasing radius decreasing radius Burggraf, Stewartson and Belcher(1971, Phys. Fluids) Radial inflow ( ), but no “overshoot”( )

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

  24. 4. 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)

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

  26. 4. Potential Vortex Above a Stationary Disk: Tornado? April 22, 2010 Texas Panhandle (H. Bluestein)

  27. 5. Boundary layer of a Rankine-Type Vortex Kuo (1971, JAS)

  28. Summary Rotating Flow / Frictional Boundary Layer Radial Inflow in BL, if Convergent,  Transport from BL to Interior Boundary Layer of Solid-Body-Rotation Vortex Application: Hurricanes Boundary Layer of Potential Vortex Application: Certain Types of Tornadoes Boundary Layer of Rankine-Type Vortex Application: Hurricanes& Certain Types of Tornadoes

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