Turbulence in Thermally-Stratified Boundary Layers over Idealized Urban Morphology

Large-eddy simulations (LESs) are used to study stratified atmospheric boundary layers over idealized urban surfaces under various conditions—unstable, neutral, and stable—ranging from free-convective to very stable regimes. A large computational domain captures large-scale coherent motions, such as horizontal convective rolls and thermal plumes in convective boundary layers (CBLs), and wave-like motions in stable boundary layers (SBLs). These interactions with urban roughness lead to complex, multiscale processes.

In urban CBLs, both the momentum correlation and the flux correlation exhibit non-monotonic trends with increasing instability due to the formation of large-scale convective rolls. Roughness length and zero-plane displacement decrease with stronger stratification. Buoyancy affects momentum transport within the roughness sublayer (RSL), reducing the impact of urban roughness and shear. This enhances upward momentum fluxes while reducing downward momentum fluxes by over 20%, even in weakly unstable conditions. Urban-type roughness promotes the formation of convective rolls under less unstable conditions compared to canonical settings.

The multiscale dynamics within urban CBLs are explored using spatial and amplitude modulation (AM) methods. Large-scale coherent structures play a key role in spatially modulating momentum fluxes in urban canopy layers (UCLs). Large-scale accelerating flows in the UCL enhance small-scale turbulence, showing a monotonic decrease in AM with increasing instability. The AM of small scales by large-scale vertical velocities is more pronounced in the UCL, with downdrafts enhancing turbulence under shear-dominant conditions and updrafts under buoyancy-dominant conditions. Building wakes dominate the AM of adjacent small-scale turbulence, with building-scale turbulence being highly influenced by AM from CBL structures. Unstable conditions significantly alter the phase relationship between large- and small-scale turbulence within UCLs.

A height-dependent scalar quantifies the nonlocal contributions within urban CBLs. With increasing instability, velocity variances and vertical heat fluxes shift from downdraft- to updraft-dominant. Despite these shifts, downdrafts primarily influence vertical momentum flux within the UCL. Wavelet analysis reveals turbulence and momentum-transporting eddies characterized by smaller length scales in downdrafts and larger scales in updrafts, which is reversed within UCLs due to urban buildings. Scale variations explain parameterization variability, with differences exceeding 100% between updrafts and downdrafts. Nonlocal processes contribute significantly to UCL turbulence and fluxes, accounting for up to 40.5% of vertical velocity variance and 56.0% of vertical heat flux.

In urban SBLs, increasing stratification confines turbulence to roughness scales and induces wave-like motions that dominate within the RSL under very stable conditions. Similarity theory with Businger-Dyer relationships, which apply under weak stability, overestimates the vertical gradients of mean velocity in more stable conditions. Dispersive flux initially increases from neutral to moderately stable conditions due to the buoyancy suppression of turbulence but declines as stability limits building-induced recirculations, forming a quiescent layer that restricts momentum and heat exchange within the UCL. Non-fully-turbulent fluctuations dominate up to 71.5% of streamwise velocity variance, 51.1% of vertical momentum flux, and 59.0% of heat flux, with wave-like motions alone contributing 46.8%, 27.2%, and 35.1%, respectively. A recovery of -5/3 scaling occurs at scales smaller than buildings, decoupled from wave-like motions, as evidenced by a distinct spectral gap.

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