The Fluid Dynamics of Tornadoes

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Presentation transcript:

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

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

Rotating Flow / No Boundary Simple Vortex

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

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

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

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

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

2. Rotating Flow/Frictional Boundary layer

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

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

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

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

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

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

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)

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

Corner Flow, End-Wall Vortex and Boundary layer

Simulations End-Wall Boundary Layer

Simulations Corner Flow ? End-Wall Boundary Layer

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

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

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

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

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)

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

End-Wall Boundary Layer Outer Flow End-Wall Boundary Layer

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

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

Vortex Breakdown Pauley and Snow (1988, MWR)

Summary Boundary Layer of a Potential Vortex  Boundary Layer of a Potential Vortex  Corner Flow and End-Wall Vortex 3. Generally Giving a Mismatch Between End-Wall and Two-Celled Vortices