More and larger wind turbines must be installed to meet ambitious targets for carbon net zero by 2050. However, in large-scale wind farms, wake interactions can lead to efficiency losses of up to 40\%. An understanding of wake dynamics is critical to improving wind farm efficiency. To this end, this thesis presents a numerical investigation of a wind turbine wake which involves two main studies of a wind turbine, in laminar flow and in a turbulent atmospheric boundary layer (ABL). Highly resolved flow field data is produced by high fidelity turbulence-resolving wind farm simulator, \texttt{WInc3D}, and allows an in-depth look at the tip-vortices and coherent structures present in the wake. Data-driven analysis methods, such as proper orthogonal decomposition and Fourier analysis, are used to extract insight from the simulation data.

In laminar flow, it is found that shear has a much greater impact on the near-wake dynamics and wake shape than thermal stratification. The mutual inductance instability is responsible for wake breakdown and coherent structures related to the wake's helical spiral and mutual inductance instability can be separated. However, the wake breakdown in a fully turbulent ABL is very different to the idealised laminar case. In a turbulent ABL, the influence of the mutual inductance instability is reduced due to a full range of overlapping excitation frequencies which lead to quick decay of the helical spiral structure. Coherent structures generated from the interaction of the wake and the ambient flow exhibit a full turbulence spectrum. Large-scale coherent structures from the ABL are especially important in re-energising the wake of an upstream and downstream turbine. Factors such as the interaction of long- and short-wave perturbations, ambient turbulence and ground effects may be responsible for the observed breakdown mechanisms in a fully turbulent ABL.