A ubiquitous feature of the high latitude ocean is the occurrence of convective clouds that are organized into two-dimensional structures known as roll clouds or cloud streets. In this paper, we present a simulation of these structures that was performed in a domain large enough to simulate numerous roll clouds and their downstream evolution at a resolution sufficient to resolve the individual convective clouds. The simulations were initialized and validated using observations of roll clouds over the Labrador Sea. The model results indicate that the secondary flow associated with the roll clouds results in significant differences in the temperature, humidity and momentum fields between the updrafts and downdrafts. The model was also able to reproduce the observed downstream evolution of the clouds as the organization of the convection changed from two-dimensional rolls to three-dimensional closed cells.