The wake dynamics behind a compliant floating offshore wind turbine (FOWT) with two alternative supporting platforms of spar buoy and barge platform are studied numerically. The computational model is based on the large eddy simulation and the use of the actuator disk model of the FOWT rotor in which the circular actuator disk is discretized with an unstructured two-dimensional triangular mesh in a structured three-dimensional Cartesian grid of the fluid domain. The wake dynamics and platform motions are calculated for laminar and turbulent inflow conditions. The flow solver is verified through a series of experimental wake measurements done behind a porous disk model and is also cross-validated against previously published results. The dynamics of the floating spar and barge structures are calculated from wavestructure interaction for three distinctive sea states. The time history of power extraction and wind force for the floating offshore wind turbine are recorded and compared against a fixed horizontal axis wind turbine. The motion of the barge platform is found to induce low-frequency modulation of the wake, whereas the spar buoy primarily displays similar wake dynamics to the fixed turbine. It is discussed how a single turbine utilizing the spar concept can be more energy efficient under the wave-induced motion. Moreover, for both laminar and turbulent inflow conditions, due to the large axial oscillation experienced by the barge concept, the turbine wake recovers more rapidly. This suggests that for a tighter spacing of the turbines in a farm, the barge platform concept can be leveraged to obtain higher energycapturing efficiency over a fixed area. K E Y W O R D S barge platform, floating wind turbines, spar buoy platform, turbulent flow, wake recovery 1 | INTRODUCTION Wind-based renewable energies are among the fastest-growing technologies within the energy sector, with the vast majority of the wind power being generated today coming from onshore wind farm locations. Offshore wind turbines have been proposed as an alternative to the conventional onshore systems. Compared with their land-based counterparts, offshore wind turbines possess a clear advantage through their access to stronger and steadier winds and their mitigated impact upon human society. 1 The majority of these offshore wind resources are located in regions