Abstract: In this paper, the frequency domain characteristic and time-varying characteristic of the RCS (Radar Cross Section) of aircraft wake vortices in clear air are analyzed. A LMP (Locally Most Powerful) detector is introduced for detection of aircraft wake vortices using coherent Doppler radar, and the analytical expressions of detection probability and false alarm probability are derived for the detector. Then the radar equations are deduced for radar detection of wake vortices. Simulation results indicate that, the detection performance of normal incidence is better than that of oblique incidence. The detection performance is improved with increasing radar range resolution, on condition that the radar observation time is long. For a wake vortex whos RCS per unit length is between -80 dBm2/m and -60 dBm2/m, the radar detection range can be between 30 km and 100 km.