A vortex wake in a Bose-Einstein condensate (BEC) may be represented via the point vortex model from classical hydrodynamics. Potential theory representations of vortices are used to examine the emergence and stability of complex vortex wakes in a BEC through the use of ordinary differential equations, which provide a great dynamical reduction with respect to the standard partial differential equation BEC models. We discuss the formation of vortex wakes, more particularly the von-Kármán street, and introduce a dynamic point vortex model that captures the stability of infinite vortex streets with a finite number of procedurally-generated vortices. The results of the dynamic model are compared to the results from the literature and from the von-Kármán street represented by a periodic strip. Further work is proposed through a discussion of the more elusive variant of the von-Kármán street experimentally observed in BECs, with its stability explored through periodic representations.