Tornadoes Eric A. Pani The University of Louisiana at Monroe

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 ~ mph Most have wind speeds < 100 mph (Source: (Source:

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: (Source: (Source:

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

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

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:

Circulation and Vorticity (Source:

Circulation and Vorticity in Natural Coordinates

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

Pressure distribution (Source:

Pressure drop a r p0p0 p∞p∞

Rough estimates Generally V max < 280 kts Let ρ = 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