Wall-attached and wall-detached eddies in proper orthogonal decomposition modes of a turbulent channel flow

To comprehensively understand the geometric and kinematic characteristics of inertial coherent motions that conform to the attached-eddy model, proper orthogonal decomposition (POD) is applied to volumetric streamwise fluctuating velocity fields in a turbulent channel flow with R e τ = 2003 being resolved by direct numerical simulation. Wall-attached POD eddies (WAPEs) or wall-detached POD eddies (WDPEs) are identified from all of the POD eigenmodes by the wall-attached or wall-detached conditions, respectively. These POD eddies can be regarded as statistical structures that make independent energy contributions. WAPEs with a wide range of scale hierarchies are found to be self-similar in both geometries and kinematics. The generalized logarithmic law of high-even-order moments contributed by self-similar WAPEs further indicates their Gaussian-like behavior. These results suggest that WAPEs are the prime statistical representatives of attached eddies. In contrast, the scale distribution of WDPEs across a wide range of flow layers is invariant and their geometric shapes are self-similar over a wide range of length scales, but the kinematic self-similarity of WDPEs is not evident.