The effects of high turbulence versus no turbulence in a sheared boundary-layer flow approaching a building are being investigated by a turbulent kinetic energy/dissipation model (TEMPEST). The effects on both the mean flow and the concentration field around a cubical building are presented. The numerical simulations demonstrate significant effects due to the differences in the incident flow. The addition of upstream turbulence results in a reduced size of the cavity directly behind the building. The velocity deficits in the wake strongly depend on the upstream turbulence intensities. The accuracy of numerical simulations is verified by comparing the predicted mean flow and concentration fields with the wind tunnel measurements of Castro and Robins (1977) and Robins and Castro (1977, 1975). Comparing the results with experimental data, the authors show that the TEMPEST model can reasonably simulate the mean flow. The numerical simulations of the concentration fields due to a source on the roof-top of the building are presented. Both the value and the position of the maximum ground-level concentration are changed dramatically due to the effects of the upstream level of turblence.