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

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Outline 1.Rotating Flow / No Boundary 2.Rotating Flow / Frictional Boundary Layer 3.Boundary Layer of a Solid-Body-Rotation Vortex 4.Boundary Layer of a Potential Vortex 5.Boundary Layer of a Rankine-Type Vortex 6. Summary

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Cylindrical Polar Coordinates 1.Rotating Flow / No Boundary

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Simple Vortex 1.Rotating Flow / No Boundary

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2. Rotating Flow/Frictional Boundary layer

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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radial tangential 4. Potential Vortex Above a Stationary Disk: Theory & Experiment Phillips and Khoo (1987, Proc. Roy. Soc. London) Inertial layer: Friction layer: Wilson and Rotunno (1986, Phys. Fluids)

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

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

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

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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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