A large-scale simulation of aerosol nucleation and growth in a turbulent mixing layer is performed and analyzed with the aim of elucidating the key processes involved. A cold gaseous stream is mixed with a hot stream of vapor, nanometer sized droplets nucleate as the vapor becomes supersaturated, and subsequently grow as more vapor condenses on their surface. All length and time scales of fluid motion and mixing are resolved and the quadrature method of moments is used to describe the dynamics of the condensing, non-inertial droplets. The results show that a region of high nucleation rate is located near the cold, dry stream, while particles undergo intense growth via condensation on the hot, humid vapor side. Supersaturation and residence times are such that number densities are low and neither coagulation nor vapor scavenging due to condensation are significant. The difference in Schmidt numbers of aerosol particles (approximated as infinity) and temperature and vapor (near unity) causes a drift of the aerosol particles in scalar space and contributes to a large scatter in the conditional statistics of aerosol quantities. The spatial distribution of the aerosol reveals high volume fraction on the hot side of the mixing layer. This distribution is due to drift against the mean and is related to turbulent mixing, which displaces particles from the nucleation region (cold side) into the growth region (hot side). Such a mechanism is absent in laminar flows and is a distinct feature of turbulent condensing aerosols.