A numerical model was developed to simulate the turbulent mixing processes that occur when a cold fluid flows into a two dimensional tank containing a warmer fluid. The process simulates the charging of a chilled water thermal energy storage tank. The numerical model employs a transient stream function-vorticity formulation to predict the streamline and temperature distributions in the tank. The turbulent effect was modeled by a two equation turbulent model using the turbulent kinetic energy and turbulent length scale equations. The results for a lower corner inlet flow show that the cold fluid will not extensively mix with the warmer fluid in the tank for Archimedean number greater than five and inlet Reynolds number less than 1000. The warm and cold fluids will thermally stratify under these conditions and limitations.