Turbulence in thermally-stratified boundary layers over idealized urban morphology

Abstract

Large-eddy simulations (LESs) are conducted to investigate stratified atmospheric boundary layers over idealized urban surfaces under unstable, neutral, or stable conditions, spanning from free-convective to very stable regimes. A large computational domain is utilized to capture large-scale coherent motions, including horizontal convective rolls and thermal plumes in convective boundary layers (CBLs), and wave-like motions in stable boundary layers (SBLs). Their interactions with urban roughness result in complex, multiscale processes.

In urban CBLs, the momentum correlation and the flux correlation show 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 influence of urban roughness and shear. It in turn enhances upward momentum fluxes while diminishes downward momentum fluxes by over 20% even in weakly unstable conditions. Urban-type roughness facilitates convective rolls formation under less unstable conditions than does in canonical settings.

Multiscale dynamics within urban CBLs is explored through spatial and amplitude modulation (AM) methods. Large-scale coherent structures are essential for spatially modulating momentum fluxes in urban canopy layers (UCLs). Large-scale accelerating flows in 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 evident in 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 highly susceptible to AM by CBL structures. Unstable conditions significantly alter the phase relationship between large- and small-scale turbulence within UCLs.

A height-dependent scalar quantifies the nonlocal contribution 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 lengthscales in downdrafts and larger scales in updrafts, 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, as much as 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 is applicable under weak stability, overestimates the vertical gradients of mean velocity in more stable conditions. Dispersive flux initially rises 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, evidenced by a distinct spectral gap.