Large scale wind farms consisting with floating offshore wind turbines (FOWTs) will be a solution for offshore wind energy industry to access more wind resources. However, wake structures and wake interactions of FOWTs subject to motions are still not yet been fully understand, especially when they are under turbulent inflow conditions with realistic turbulent intensities. These will be critical for designing floating offshore wind farms. Note that the majority of previous research are conducted with single rotor using models having relatively low fidelities and/or focusing on laminar inflow conditions. To advance the knowledge about wake and wake interactions of FOWTs, numerical studies about rotors of FOWT with prescribed harmonic surging motions are conducted in this thesis project with high fidelity CFD models, namely large eddy simulation (LES) coupled with actuator line model (ALM). Cases with single rotor without controller, dual rotors in tandem without controller, and dual rotors in tandem with controller are simulated with various of settings, including different surging settings and different inflow turbulence intensities. For the cases with single rotor without controller, it is found that the differences of wake structures between fixed and surging rotors are pronounced when under laminar inflow conditions, where the periodic structures related to the harmonic surging motions can be detected straightforwardly; while the differences are much less significant when under inflow conditions with realistic turbulence intensities, and the periodic structures are clearly revealed only after phase-locked averaging. Moreover, surging cases with laminar inflow conditions have wake recovery rates which are significantly higher than the fixed case with laminar inflow; however, with turbulent inflow, wake recovery rates for surging cases are only slightly higher than the fixed case. For the cases with dual rotors without controller, it is found that the wake interaction modes between the two rotors are significantly affected by the surging settings for the laminar cases, while the turbulent cases are insensitive. However, the power performances of the downstream rotors will be increased slightly with surging upstream rotors for the turbulent cases. For the cases with dual rotors with controller, it is found that the implemented simple controller cannot improve the performances of the rotors as designed due to the large rotational inertia, and thus the modes of wake interactions are not altered a lot. However, the downstream rotors' operational parameters were successfully changed to more desirable values by the controller, demonstrating the controller's potential for numerical analysis of wake interactions between wind turbine rotors. The findings of this effort demonstrates that the wake structures due to the surging motions of FOWT rotors will be smeared out by the ambient turbulence; and to achieve better power performances, more advanced controlling strategies may have to be implemented for FOWTs subject to surging motions.