A study is made of the two-dimensional buoyant surface discharge into an ambient body of water. The numerical study is based on an initial boundary value problem using the full Navier-Stokes and diffusion equations. A turbulence model using the Munk-Anderson parameterization formula for density stratification effect is also incorporated. The results show the establishment of a surface density current with strong surface convergenc and downwelling near the front. Comparison is made wth the field experiments of Garvine and Monk on a small-scale oceanic front in Long Island Sound. Excellent agreement is obtained.