Effect of computer-generated turbulent wind field on trajectory of compact debris: A probabilistic analysis approach

Abstract

A model and numerical algorithm is developed to simulate wind-borne debris trajectories in a fully-developed atmospheric boundary layer wind. The model works in two dimensions and makes use of synthetically-generated turbulence time histories; it accounts for variable mean velocity field with elevation and turbulence. The simulation of a partially coherent wind field was based on the wave superposition method (Di Paola, 1998) [1]. For the simulation of the turbulence field, a simplified approach is proposed. First, turbulence is generated at discrete points located on the “inlet boundary” of the field; second, turbulence is propagated through the field using either Taylor’s “frozen turbulence” hypothesis or a simplified “Eulerian–Lagrangian” formulation. The latter term is used to emphasize that an expression is employed to approximately replicate the features of the Lagrangian turbulence wind spectrum (for high-speed moving objects), even though turbulence is still synthetically generated on a large portion of the field at all times, from an Eulerian point of view. After generating the wind field, the trajectory of compact objects is estimated by means of a point mass dynamic model, converted to state-space form and integrated by fifth-order Runge–Kutta method.The numerical model is applied to the study of the risk of impact by wind-borne debris against tall building facades, recently investigated by the authors for uniform non-turbulent wind field only. The analysis is conducted by using the computer-generated wind field to estimate “universal probability curves” (probability-of-impact curves) for compact debris, conditional on the initial distance of the object from the building before takeoff. Both qualitative and quantitative variations are noted in comparison with previous results.