Remote sensors like Doppler lidars can map the winds with high accuracy and spatial resolution. One shortcoming of lidars is that the radial velocity measured by the lidar does not give a complete picture of the windfield necessitating additional data processing to reconstruct the windfield. Most of the popular vector retrieval algorithms rely on the homogenous wind field assumption which plays a vital role in reducing the indeterminacy of the inverse problem of obtaining Cartesian velocity from radial velocity measurements. Consequently, these methods fail in situations where the flow is heterogeneous e.g., Turbine wakes. Alternate methods are based either on statistical models (e.g., optimal interpolation [1]) or computationally intensive four dimensional variational methods [2]. This study deals with a 2D variational vector retrieval for Doppler lidar that uses the radial velocity advection equation as an additional constraint along with a tangential velocity constraint derived from a new formulation with gradients of radial velocity. The retrieval was applied on lidar data from a wind farm and preliminary analysis revealed that the algorithm was able to retrieve the mean wind field while preserving the small scale flow structure.