Modelling wind fields and debris flight in tornadoes

Abstract

This paper describes the derivation of a simple yet realistic engineering model of tornado wind and pressure fields. This novel model is shown to be capable of providing a method for predicting wind speed and pressure time histories and debris impact energies that can ultimately be used in the development of a rational risk-based design methodology for tornado wind loads on buildings. A stationary one-cell tornado vortex is first considered, and the circumferential and vertical velocities and pressure profiles derived from a simple assumption for radial velocity (that is bounded in the radial and vertical directions) and the use of the Euler equations. The generalisation of this model to a two-cell tornado form is then set out. This model is then used to investigate the trajectories of wind borne debris in tornado wind fields, and for the first time, this analysis reveals the important dimensionless parameters of the problem and the parameter boundary between falling and flying debris. An asymptotic long time solution for debris paths is also derived.