  The pioneering work of G.I. Taylor on the turbulent dispersion of aerosols is
exactly one century old and provides an original way of introducing both
diffusive processes and turbulence at an undergraduate level. Light enough
particles transported by a turbulent flow exhibit a Brownian-like motion over
time scales larger than the velocity correlation time. Aerosols are therefore
subjected to an effective turbulent diffusion at large length scales. However,
the case of a source of pollutant much smaller than the integral scale is not
completely understood. Here, we present experimental results obtained by
undergraduate students in the context of the COVID-19 pandemic. The dispersion
of a smoke of oil droplets by a turbulent flow is studied in a wind tunnel
designed for pedagogical purposes. It shows a ballistic-like regime at short
distance, followed by Taylor's diffusive-like regime, suggesting that the
continuous cascade is bypassed. Accordingly, measurements show that the CO$_2$
concentration emitted when breathing typically decays as the inverse squared
distance to the mouth, which is not the law expected for a diffusion. The
experiment offers the possibility for students to understand the role of
fluctuations in diffusive processes and in turbulence. The non-linear diffusive
equations governing aerosol dispersion, based on a single correlation time,
allow us to model the airborne transmission risk of pathogens, indoors and
outdoors. We discuss the pedagogical interest of making students work on
applied scientific problems, as the results obtained in this study have been
used to provide public health policy recommendations to prevent transmission in
French shopping malls.
