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Three-dimensional simulations of plasma turbulence have been run using the STORM module of BOUT + + in a simple slab geometry aimed at representing a single, isolated tokamak divertor leg. Turbulence is driven primarily by the Kelvin-Helmholtz mechanism due to the sheared ExB flow that forms around the separatrix due to strong radial gradients in the sheath potential which arise from strong radial gradients in the electron temperature. The turbulence forms a mixing layer around the separatrix which spreads heat and particles into the private-flux region. The resulting spread of the electron heat flux is within the experimental range measured on MAST. An effective thermal transport coefficient which is approximately 10% of the Bohm value is measured from the simulations. When a transport coefficient of this magnitude is used in a diffusive axisymmetric simulation, the time-averaged radial profiles share similar features to the full turbulence simulation.