Although conventional Doppler ultrasound is widely used for quantifying blood flow, it is restricted by its low sensitivity to detect slow flow. The incorporation of ultrafast ultrasound and spatial-temporal clutter filters can not only extensively boost the Doppler sensitivity to low-velocity slow flow but also facilitate the development of advanced 3-D Doppler techniques. In this work, we propose a novel 3-D Doppler method which extends 2-D imaging to 3-D through the continuous mechanical translation of a linear transducer. The viability of this method is assessed by simulations with the aids of a theoretical model. The combination of simulations and the theoretical model provides unique insights into the inherent mechanisms involved in the performance of this 3-D Doppler method and the roles of factors, such as tissue vibration characteristics, blood flow velocity, elevational point-spread-function profile, probe translating speed, and signal energy ratios.