Assessing the methods of extracting attached eddies

The success of the attached eddy model (AEM) and the search for typical representations of attached eddies call for the development of various methods for extracting attached eddies. However, previous studies have not systematically compared these methods in terms of their statistical wall laws for different physical quantities. In particular, the wall laws for arbitrary moments of the velocity gradient and higher-order velocity derivatives in the logarithmic region, derived in our previous study, have not been checked by using these various methods. In the present study, we focus on three methods, that is, the spectral filtering based on streamwise wavelength (SF), proper orthogonal decomposition (POD), and clustering methodology (CM), and assess their ability of capturing the statistical characteristics predicted by the AEM. It is found that based on two-dimensional instantaneous flow fields, the SF method demonstrates the best performance in capturing the statistical laws of velocity gradients and Hessians, followed by CM, while POD proves inadequate for capturing the scaling laws of velocity gradients and Hessians. Moreover, a parametric analysis is carried out to discuss in detail the specific effects of various parameters in each method on the statistical moments. These results are expected to identify key parameters in these methods and contribute to their improvement, enabling better capture of the statistical laws predicted by the AEM.