Characterizing Superstructures in Rough-Wall Turbulence

In this paper, we investigate large-scale superstructures over a k-type homogeneous rough wall (k_s+ = 209) at a speed of 1.3 × 10^6 Rem−1, under varying pressure gradient conditions characterized by Clauser parameters ranging from beta = −0.6 (Favorable Pressure Gradient) to beta = 0.98 (Adverse Pressure Gradient). Time-resolved stereoscopic wall-parallel PIV measurements, combined with two-point spatial and temporal correlation analyses, reveal the presence of predominantly streamwise-aligned large-scale structures. While these correlations qualitatively capture the spatial and temporal coherence of the flow, only subtle variations are observed across different pressure gradient conditions. To gain deeper insights, kernelized Residual Dynamic Mode Decomposition (kResDMD) was employed to extract coherent modes that are not superstructures themselves but served as the skeletal representation of these structures. This modal characterization enabled us to quantify pressure gradient effects on structure distribution, organization, orientation, and frequency content, providing a more comprehensive description of superstructure dynamics in rough-wall turbulent boundary layers.