This work presents the development of computational models that capture vorticity generation and turbulent diffusion within wind and hydrokinetic turbine farms. The use of vortex methods is examined as an alternative for modeling turbulent wakes and rotor-wake interaction. The vorticity-velocity formulation of the Navier-Stokes equations are simulated by a hybrid Lagrangian-Eulerian method involving both fluid particles that carry vorticity and mesh discretizations which enable an efficient solution to N-body vorticity dynamics. A "mesh free" particle-strength-exchange (PSE) algorithm and a "particle-mesh" vortex-in-cell (VIC) algorithm are implemented for a series of benchmarks to verify the simulation method for low Reynolds number flows, including: vortex ring dynamics, flow over bluff bodies, and a 3D wing. These examples are presented on a variety of computer architectures, with support for distributed-memory parallelism, multi-core, and GPGPU computing. The scalability and stability of these proposed vortex methods shows potential for modeling the large range of scales present between rotor-scale and farm-scale hydrodynamics. The desired feature of this methodology is faithful prediction of unsteady phenomenon, capture of vortex shedding, and tracking the evolution of vortical structures as they evolve and interact with immersed structures and ambient turbulent flow.