The wake of a horizontal-axis wind turbine was studied at a Reynolds number of $Re_D=4\times 10^6$ with the aim of revealing the effects of the tip speed ratio, $\lambda$, on the wake. Tip speed ratios of $4\lt \lambda \lt 7$ were investigated and measurements were acquired up to 6.5 diameters downstream of the turbine. Through an investigation of the turbulent statistics, it is shown that the wake recovery was accelerated due to the higher turbulence levels associated with lower tip speed ratios. The energy spectra indicate that larger broadband turbulence levels at lower tip speed ratios contributes to a more rapidly recovering wake. Wake meandering and a coherent core structure were also studied, and it is shown that these flow features are tip speed ratio invariant, when considering their Strouhal numbers. This finding contradicts some previous studies regarding the core structure, indicating that the structure was formed by a bulk rotor geometric feature, rather than by the rotating blades. Finally, the core structure was shown to persist farther into the near wake with decreasing tip speed ratio. The structure’s lifetime is hypothesised to be related to its strength relative to the turbulence in the core, which decreases with increasing tip speed ratio.