1. Tornadoes Eric A. Pani The University of Louisiana at Monroe

2. Background  Definition: a violently rotating column of air that extends to the ground from a cumuliform cloud  Visible funnel may not be present every time  Funnel cloud if rotation does not reach ground  Most rotate cyclonically  Statistics: Average width ~ 100 m Average path length ~ 1-2 miles Average forward speed ~ 10- 20 mph Most have wind speeds < 100 mph (Source: http://www.motorminute.com/Mixed_Nutz/Tornado.gif) (Source:http://www.zonezero.com/exposiciones/road/images/eleventh/tornado.jpg

3. Life cycle Dust-whirl stage: first sign as dust swirling upward from surface and short funnel from cloud base Organizing stage: downward descent of funnel and increased intensed Mature stage: funnel reaches greatest width and nearly vertical Shrinking stage: decreasing funnel width, increasing tilt as base lags Decay stage: vortex stretches into rope May not go trough all stages (Source: http://wings.avkids.com/Book/Atmosphere/Images/tornado.gif) (Source: http://www.redriver.net/tornado/tornado.jpg) (Source: http://tornado.sfsu.edu/geosciences/StormChasing/cases/Miami/MiamiWallcloud.GIF)

4. Circulation and Vorticity Circulation is line integral (counterclockwise) about a contour of velocity component tangent to the contour

5. Solid Body Rotation Suppose a circular disk of radius r is rotating at an angular velocity Ω about the z axis is solid body rotation dl r dθdθ

6. Problem For a large tornado, C ~ 5  10 4 m 2 s -1 If r ~ 100 m, what is the value of Ω and V? C = 2πΩr 2 and V= Ωr Ω = C/(2πr 2 ) Ω = (5  10 4 )/(2π(100) 2 )=0.8 s -1 V = (0.8)(100) = 80 ms -1 ~160 kts (Source: http://www.usatoday.com/weather/gallery/tornado/wtor4a.jpg)

7. Circulation and Vorticity (Source: http://www.nws.noaa.gov/om/all-haz/Double%20Tornado%20Hi.jpg)

8. Circulation and Vorticity in Natural Coordinates

9. Combined Rankin Vortex r=a uniform vorticity irrotational environment V r V max a

10. Pressure distribution (Source: http://www.ametsoc.org/AMS/image/challeng/tornado.gif)

11. Pressure drop a r p0p0 p∞p∞

12. Rough estimates Generally V max < 280 kts Let ρ = 1.275 kg m -3 Then p ∞ – p 0 = ρV max 2 =(1.275)(130) 2 =215 mb Generally taken to be ~ 100 mb Vertical velocities substantial (~ 80 m/s) and not necessarily in core Inflow velocities may reach 50 m/s near ground