Evolution and instability of the tip vortices behind a yawed wind turbine

Yaw control can effectively enhance wind farm power output, but the vorticity distribution and coherent structures in yawed turbine wakes remain poorly understood. We propose a physical model capable of accurately predicting tip vortex dynamics from their generation to destabilisation. This model integrates a point vortex framework with advanced blade element momentum theory and vortex cylinder theory for yawed turbines. Comparisons with large eddy simulations demonstrate that the model effectively predicts the vorticity distribution of tip vortices and the wake profile of yawed turbines. Finally, we employ sparsity-promoting dynamic mode decomposition to analyse the dynamics of the far wake. Our analysis reveals four primary mode types: (i) the averaged mode; (ii) shear modes; (iii) harmonic modes; and (iv) merging modes. Under yawed conditions, these modes become asymmetric, leading to interactions between the tip and root vortex modes. This direct interaction plays a critical role during the formation process of the counter-rotating vortex pair observed in yawed wakes.