Turbulent shear flow beneath a flat free surface driven by a surface stress is simulated numerically to gain a better understanding of the hydrodynamic processes governing the scalar transfer across the air-water interface. The simulation is posed to mimic the subsequent development of a wind-driven shear layer as in a previous experiment except that the initiation of the surface waves is inhibited, thus focusing on the boundary effect of the stress-imposed surface on the underlying turbulent flow and vice versa. Despite the idealizations inherent in conducting the simulation, the computed flow exhibits the major surface features, qualitatively similar to those that appear in the laboratory and field experiments. Two distinct surface signatures, namely elongated high-speed streaks and localized low-speed spots, are observed in the simulated flow. Including temperature as a passive tracer and describing an upward heat flux at the surface, we obtain high-speed streaks that are colder and low-speed spots that are warmer than the surrounding regions. The high-speed streaks, arranged with somewhat equal cross-spacing of centimetres scale, are formed by an array of streamwise jets within the viscous sublayer immediately next to the surface. Beneath the streaks, counter-rotating streamwise vortex pairs are observed among other prevailing elongated vortices. However, they are significantly shorter in length and more irregular than their corresponding high-speed streaks at the surface. Accompanying the more organized high-speed streaks, localized regions of low streamwise velocity emerge randomly on the surface. These low-speed spots are attributed to strong upwelling flows which disrupt the viscous sublayer and also bring up the submerged fluids of low streamwise velocity. The occasional interruptions of the streamwise high-speed jets by the upwelling flows account for bifurcation or dislocation of the surface streaks. Statistics of the turbulence are presented and their implications for the formation of the flow structures are discussed.