Spectral Proper Orthogonal Decomposition of Coherent Structure and Energy Transfer in Urban Convective Boundary Layers

This study uses spectral proper orthogonal decomposition ({SPOD}) to analyze how large-scale motions (LSMs) modulate small-scale turbulence in the urban boundary layer under unstable stratification. Dominant LSMs extracted by SPOD show increased vertical extent and inclination at higher elevations. Results indicate that unstable stratification intensifies near-ground turbulence and enhances the organizational role of LSMs. In more unstable condition, the energy fraction and modulation effect of LSMs are enhanced, accompanied by a shift in the dominant frequency towards lower values, a contraction of the correlation scale, and a more vertical orientation of the structures. The SPOD reconstruction accurately captures the dominant characteristics of LSMs, especially under strong stability, where the results closely match those of the original flow. LSMs at different heights exhibit distinct spatial distributions and inclination angles, with greater vertical extent and larger inclination at higher elevations. Unstable stratification strengthens the vertical development of LSMs, increasing their modulation of near-surface turbulence. These findings provide new insights for understanding and modelling LSMs and energy transport processes in urban boundary layer turbulence.