A two-dimensional, third-order turbulence closure model is developed to study the atmospheric boundary layer with one horizontal direction of inhomogeneity. Use of the Flux Corrected Transport scheme leads to numerical stability with low nonphysical diffusion. The case of a sea breeze circulation is simulated. The turbulence structure of the flow is described. The turbulent kinetic energy is included in the energetics of the circulation. The relations between convection and the dynamics of the sea breeze, including the velocity of the inland penetration of the front, are studied.