To quantify the turbulent transport at gray zone length scales between 1 and 10 km, the Lagrangian evolution of the CONSTRAIN cold air outbreak case was simulated with seven large eddy models. The case is characterized by rather large latent and sensible heat fluxes and a rapid deepening rate of the boundary layer. In some models the entrainment velocity exceeds 4 cm/s. A significant fraction of this growth is attributed to a strong longwave radiative cooling of the inversion layer. The evolution and the timing of the breakup of the stratocumulus cloud deck differ significantly among the models. Sensitivity experiments demonstrate that a decrease in the prescribed cloud droplet number concentration and the inclusion of ice microphysics both act to speed up the thinning of the stratocumulus by enhancing the production of precipitation. In all models the formation of mesoscale fluctuations is clearly evident in the cloud fields and also in the horizontal wind velocity. Resolved vertical fluxes remain important for scales up to 10 km. The simulation results show that the resolved vertical velocity variance gradually diminishes with a coarsening of the horizontal mesh, but the total vertical fluxes of heat, moisture, and momentum are only weakly affected. This is a promising result as it demonstrates the potential use of a mesh size‐dependent turbulent length scale for convective boundary layers at gray zone model resolutions.