Urban turbulence is a typical form of rough-wall turbulence, in which turbulent motions within the roughness sublayer are strongly influenced by obstacle geometry. Based on large-eddy simulations (LES) and space-scale filtering in wavelet space, this study investigates the energy contributions and interscale interactions associated with obstacle-induced motions under various flow configurations, including different obstacle layouts, height variations, and wind directions. The results reveal that sub-filtered scale (SFS) contributions to turbulent kinetic energy (TKE) generally peak within the canopy layer, with the peak height varying depending on the flow configuration, and decrease sharply above the roof level ( \(z/H_{max} = 1\) ). In contrast, the SFS Reynolds stress peaks in the near-wall region and exhibits a secondary maximum near the roof level. At a cut-off scale equal to one-quarter of the canyon scale ( \(n=3\) ), the sub-filtered scale (SFS) contributions, based on the Haar wavelet basis, account for approximately 20% or more of the total TKE and Reynolds stress across the entire vertical domain of interest ( \(z/H \le 2.5\) ). Following the framework of Meneveau (Meneveau in J Fluid Mech 232:469–520, 1991), interscale interactions between sub-canyon and larger-scale motions are quantified using the effective eddy viscosity defined in the wavelet space. The vertical profiles of SFS energy and effective eddy viscosity demonstrate significant sensitivity to obstacle layout within the canopy layer and to obstacle height near the roof level. These findings advance the understanding of small-scale motions and their role in wall turbulence, emphasizing the necessity of capturing vertical variability and sub-filter scale dynamics in urban boundary layer simulations to improve turbulence modeling.
