This paper investigates the characteristics of turbine wake which is the major factor determining the turbulence in wind farm and overall wind farm performance. Using the lattice Boltzmann method (LBM) and the large eddy simulation (LES) approach, dynamic simulations of detailed fluid flow and wake trajectory induced by the MEXICO wind turbine were carried out. Moreover, with the help of adaptive mesh refinement (AMR) method, the lattice units were allowed to be automatically refined to allocate more grid points on the solid walls and in the wake region. The simulation results were firstly compared with the experimental data for validation of the numerical model, as well as for investigation of the impact of sub‐grid scale (SGS) turbulence models. Within the present modeling framework, the characteristics of transient wake propagation, detailed flow field, and rotor‐tower interaction were investigated, and the effect of tip‐speed ratio was also analyzed. The present work indicates that, with a suitable SGS turbulence model, the LBM‐LES method is an effective way for dynamic simulations of wake structures induced by a wind turbine with a rotating rotor.