The paper considers the problem of identifying the aircraft wake vortices by lidar scanning data. The aircraft wake vortices are extremely hazard to flight safety and Doppler coherent scanning lidars are actively used for their identification. Since the Doppler lidar measures only the radial component of the air flow velocity, the problem of identifying the wake vortex position by lidar measurement data arises. The paper considers an approach based on calculating the gradient of the scalar lidar measurements field. To calculate the gradient, it is proposed to use the Sobel operator (or the Scharr operator). The selection of points of anomalous gradient behavior corresponding to the wake vortex region is performed according to a given threshold level. After that, a clustering procedure is performed using the DBSCAN algorithm to localize each vortex and filter out noise measurements. The position of each vortex in the wake is calculated as a simple geometric center of the identified clusters. It is shown that clustering by the value of the full gradient and the value of the vertical gradient give close results.