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The Mechanics of Falling Hailstones and Hailswaths Kevin Vermeesch and Ernest Agee Department of Earth and Atmospheric Sciences, Purdue University Objectives Cases and Model Results •Develop a set of mechanical equations for calculating hailstone fall velocities and characteristics for a variety of thunderstorm and atmospheric conditions Cases Testing Fall Speeds •Plot hailswaths for real atmospheric events and compare with model results Hailstone Fall Velocity (m/s) Physical Properties in the Model Equations •Density profile of atmosphere •Diameter and mass of spheroidal hailstones •Drag coefficient for subcritical Reynolds number flow Case 1 Parameters Hailstone Fall Velocity at Ground Parameter 35 Value 30 25 hailstone diameter (dstone) 0.75 in hailstone density (ρstone) 900 kg m-3 drag coefficient (CD) 0.5 air density (ρair) 0.900 kg m-3 initial height AGL (z0) 7.0 km 20 15 10 5 0 1 2 3 4 5 Case Num ber •Translational speed of supercell thunderstorm •Updraft velocity profile of the supercell thunderstorm Information for Cases 2-5 •Rotational velocity profile of embedded mesocyclone •Spherical vs. non-spherical hailstone and related Re and CD Hailstone Fall Time Re < Rec Fall Time (s) 450 Re > Rec 400 Case Number Difference from Case 1 Case 2 air density reduced by 50% (ρair = 0.450 kg m-3) Case 3 air density exponentially increases towards the ground [ρair = ρ0 exp(-z0 / Hρ)] Case 4 hailstone diameter is increased to 1 inch and updraft velocity (w) = 20.0 m s-1 Case 5 hailstone diameter is increased to 1 inch, air density exponentially increases towards the ground [ρair = ρ0 exp(-z0 / Hρ)] and updraft velocity (w) = 20.0 m s-1 350 300 250 200 Hailswaths Knight and Knight (2005), Figure 9 Hailstone shapes range from being nearly spherical and smooth to very irregular, containing knobs, lobes, or spikes on their surface. The smooth stones fall under conditions of subcritical Reynolds flow, while the irregular shapes may achieve supercritical flow conditions. Graphical verification of model terminal velocity with Knight and Knight (2001) Size-sorted hailswath produced by model 1 2 3 4 5 Case Num ber In a size-sorted hailswath, the largest hail lands closest to the mesocyclone (or tornado track if present). The dimensions of the swath are a function of the thunderstorm’s rotational velocity (vθ), translational velocity (u), and mesocyclone radius. The image on the right shows a portion of the mesocyclone and underlying wall cloud, flanked by a spectacular hailshaft that produces the hailswath. References Knight, C.A. and N.C. Knight, 2001: Hailstorms. Severe Convective Storms, Meteor. Monogr., No. 50, Amer. Meteor. Soc., 223-249. Knight, C.A. and N.C. Knight, 2005: Very large hailstones from Aurora, Nebraska. Bull. Amer. Meteor. Soc., 86, 1773-1781. Knight and Knight (2001), Figure 6.2 3 April 1974 tornado tracks and hailswath in Indiana