Above a solid bottom beneath non-linear shallow water waves, it is found that due to turbulence asymmetry between subsequent wave half-cycles, a net drift is generated in the direction opposite of surface wave propagation. This phenomenon is investigated by means of numerical solution of the incompressible Navier-Stokes equations. With the aid of a turbulence model within a large eddy simulation, turbulent streaming is observed at a higher Reynolds number than has previously been considered. During steady intervals when wave-average Reynolds and viscous stresses are in balance, the expected streaming behavior is observed, with direct dependence on Re. Included with these findings is the interesting absence of bottom shear associated with this streaming. The behavior of turbulent streaming during stress imbalance is also explored and a mechanism for streaming spin-up proposed.