Energy exchanges between coherent modes in the near wake of a wind turbine model at different tip speed ratios

Abstract

In this work we investigate the spatio-temporal nature of various coherent modes present in a wind turbine wake using a combination of new particle image velocimetry experiments and data from Biswas & Buxton (J. Fluid Mech., vol. 979, 2024, A34). A multiscale triple decomposition of the acquired velocity field is sought to extract the coherent modes and, thereafter, the energy exchanges to and from them are studied using the multiscale triple decomposed coherent kinetic energy budgets developed by Baj & Buxton (Phys. Rev. Fluids, vol. 2, 2017, 114607). Different frequencies forming the tip vortex system (such as the blade passing frequency, turbine's rotational frequency and their harmonics) are found to be energised by different sources such as production from the mean flow or nonlinear triadic interaction or both, similar to the primary, secondary or the mixed modes discussed in Biswas et al. (J. Fluid Mech., vol. 941, 2022, A36). The tip vortex system forms a complex network of nonlinear triadic energy transfers, the nature and the magnitudes of which depend on the tip speed ratio ( $\lambda$ ). Contrastingly, the modes associated with the sheddings from the nacelle or tower and wake meandering are found to be primarily energised by the mean flow. We show that the tip vortex system exchanges energy with the mean flow primarily through the turbine's rotational frequency. In fact, the system transfers energy back to the mean flow through the turbine's rotational frequency at some distance downstream marking the onset location of wake recovery ( $x_{wr}$ ). Here $x_{wr}$ is shown to reduce with $\lambda$ due to stronger interaction and earlier merging of the tip vortices at a higher $\lambda$ .