The observed widths of cloud droplet spectra in adiabatic volumes of natural clouds have been a conundrum in cloud physics from the early days of in-situ cloud observations. Observed spectral widths are often in the range of 1 to 2 microns, whereas adiabatic parcel calculations suggest widths up to only a few tenths of 1 micron. We use a 1D Eulerian updraft model with Lagrangian particle–based microphysics (introduced in Grabowski et al. JAS 2025) to study the impact of cloud turbulence on droplet formation and diffusional growth. The model either includes or excludes effects of cloud turbulence. The impact of turbulence is simulated using a stochastic model of vertical velocity fluctuations that drive supersaturation fluctuations experienced separately by each superdroplet. The specific setup considers shallow cumulus clouds growing from a turbulent convective boundary layer and featuring cloud base updrafts between 1 and 4 m s^-1. The focus is on contrasting adiabatic spectral broadening in pristine and polluted environments, and on comparing modeling results with cloud observations. Turbulence significantly impacts CCN activation and droplet diffusional growth above the cloud base and leads to an increased adiabatic spectral width aloft. The impact is moderate for polluted clouds, but spectral widths in pristine conditions are up to several times larger than those with no turbulence. In contrast, adiabatic simulations without turbulence typically feature wider droplet spectra in polluted clouds. The difference comes from a larger range of activated CCN and a larger magnitude of supersaturation fluctuations for the same vertical velocity fluctuations because of a larger phase relaxation time in pristine conditions.

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