Incorporating Sweeps and Ejections into Lagrangian Stochastic Models of Spore Trajectories Within Plant Canopy Turbulence: Modeled Contact Distributions Are Heavy-Tailed

Abstract

The turbulent dispersal of fungal spores within plant canopies is very different from that within atmospheric boundary-layers and closely analogous to dispersal within turbulent mixing-layers. The process is dominated by the presence of large coherent flow structures, high-velocity downdrafts (sweeps) and updrafts (ejections), that punctuate otherwise quiescent flow. Turbulent dispersion within plant canopies is best predicted by Lagrangian stochastic (particle-tracking) models because other approaches (e.g., diffusion models and similarity theory) are either inappropriate or invalid. Nonetheless, attempts to construct such models have not been wholly successful. Accounting for sweeps and ejections has substantially worsened rather than improved model agreement with experimental dispersion data. Here we show how this long-standing difficulty with the formulation of Lagrangian stochastic models can be overcome. The new model is shown to be in good agreement with data from a carefully controlled, well-documented wind-tunnel study of scalar dispersion within plant canopy turbulence. Equally good agreement with this data is obtained using Thomson's (1987) Gaussian model. This bolsters confidence in the application of this simple model to the prediction of spore dispersal within plant canopy turbulence. Contact distributions—the probability distribution function for the distance of viable fungal spore movement until deposition—are predicted to have “heavy” inverse power-law tails. It is known that heavy-tailed contact distributions also characterize the dispersal of spores which pass through the canopy turbulence and enter into the overlying atmospheric boundary-layer. Plant disease epidemics due to the airborne dispersal of fungal spores are therefore predicted to develop as accelerating waves over a vast range of scales—from the within field scale to intercontinental scales. This prediction is consistent with recent analyses of field and historical data for rusts in wheat. Such plant disease epidemics are shown to be governed by space-fractional diffusion equations and by Lévy flights.