Estimating the Poynting flux of Alfv\'enic waves in polar coronal holes across Solar Cycle 24

Alfv\'enic waves are known to be prevalent throughout the corona and solar wind. Determining the Poynting flux supplied by the waves is required for constraining their role in plasma heating and acceleration, as well as providing a constraint for Alfv\'en wave driven models that aim to predict coronal and solar wind properties. Previous studies of the Alfv\'enic waves in polar coronal holes have been able to provide a measure of energy flux for arbitrary case studies. Here we build upon previous work and take a more systematic approach, examining if there is evidence for any variation in vertical Poynting flux over the course of the solar cycle. We use imaging data from SDO/AIA to measure the displacements of the fine-scale structure present in coronal holes. It is found that the measure for vertical Poynting flux is broadly similar over the solar cycle, implying a consistent contribution from waves to the energy budget of the solar wind. There is variation in energy flux across the measurements (around 30\%), but this is suggested to be due to differences in the individual coronal holes rather than a feature of the solar cycle. Our direct estimates are in agreement with recent studies by \cite{Huang_2023,Huang2024} who constrain the vertical Poynting flux through comparison of predicted wind properties from Alfv\'enic wave driven turbulence models to those observed with OMNI at 1~AU. Taken together, both sets of results points towards a lack of correlation between the coronal Poynting flux from waves and the solar cycle.