On the roles of clustered inertial particles in inter-phase, cross-scale momentum transfer

Inter-phase, cross-scale transfer of turbulence kinetic energy (TKE) of two-way coupled homogeneous isotropic turbulence is examined using a wavelet multiresolution analysis. Locally in space, clusters of the critical particles (St_k = 1) are not definite energy sources or sinks. Cross-scale transfer estimated using the subfilter-scale energy flux Π_SFS does not indicate a definite direction of energy transfer in the spectral space at positions where St_k = 1 particles accumulate. Local Π_SFS is not necessarily amplified by the clusters, although the mean downscale transfer is enhanced. Wavelet statistics conditioned on coarse-grained number density support the same conclusions. Clusters of St_k = 1 particles are associated with a co-existence of down- and upscale energy transfer.  Regions devoid of St_k = 1 particles are characterized by the in-scale energy transfer (Π_SFS ≈ 0), while the inverse is not true. The critical particles create nonlocal modulations of turbulence, although they are accumulated locally in space. In addition, the analysis supports \textit{a priori}, a validity of the subgrid-scale (SGS) Stokes number useful for analyzing the SGS modeling of two-way coupled particle-laden turbulence.