The macroscopic flow properties of pure He II are probed in the limit of zero temperature using an oscillating grid. As the oscillation amplitude passes a first critical threshold, the resonant frequency starts decreasing but the flow remains nondissipative. Beyond a second critical amplitude, the flow undergoes a transition to turbulence and becomes dissipative. Nonlinearity and hysteresis observed between the thresholds are attributed to a boundary layer of quantized vortices.