Transit time broadening is a major limitation in pulsed wave (PW) Doppler, especially when the angle between the flow direction and the ultrasound beam is large. The associated loss in frequency resolution may give severe overestimation of blood velocities, and finer details in the spectral display are lost. By using plane wave transmissions and parallel receive beamforming, multiple PW Doppler signals can be acquired simultaneously in a 2-D region. This enables tracking of the moving blood scatterers over a longer spatial distance to limit transit time broadening. In this work, the new method was tested using in vitro ultrasound recordings from a flow phantom, and in vivo recordings from a human carotid artery. The resulting 2-D tracking Doppler spectra showed significantly reduced spectral broadening compared with Doppler spectra generated by Welch's method. The reduction in spectral broadening was 4-fold when the velocity was 0.82 m/s and the beam-to-flow angle was 62°. A signal model was derived and the expected Doppler power spectra were calculated, showing good agreement with experimental data. Improved spectral resolution was shown for beam-to-flow angles between 40° and 82°.