Non-Hermitian potentials, as known since a decade, can favor unidirectionality of the flows in one and two-dimensional systems. Inspired by such counterintuitive property of non-Hermitian potential, we propose a novel concept of PT-vector fields to manipulate the field flows in two- (or higher) dimensional systems. The idea is based on designing complex potentials favoring arbitrary vector fields of directionality 𝑝⃗(𝑟⃗) with desired shapes and topologies. To achieve this, we derive a new mathematical tool referred as local Hilbert transform. We study interesting cases of such vector fields in the form of sink, vortex, and circular channel, constructed from different background patterns using local Hilbert transform. This new concept provides a precise control over the dynamics of the probe fields, which may have potential applications in technological systems.