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Non-stationarity is the rule in the atmospheric boundary layer (ABL). Undersuch conditions, the flow may experience departures from equilibrium with theunderlying surface stress, misalignment of shear stresses and strain rates, andthree-dimensionality in turbulence statistics. Existing ABL flow theories areprimarily established for statistically stationary flow conditions and cannotpredict such behaviors. Motivated by this knowledge gap, this study analyzesthe impact of time-varying pressure gradients on mean flow and turbulence overurban-like surfaces. A series of large-eddy simulations of pulsatile flow overcuboid arrays is performed, programmatically varying the oscillation amplitude$\alpha$ and forcing frequency $\omega$. The analysis focuses on bothlongtime-averaged and phase-dependent flow dynamics. Inspection oflongtime-averaged velocity profiles reveals that the aerodynamic roughnesslength $z_0$ increases with $\alpha$ and $\omega$, whereas the displacementheight $d$ appears to be insensitive to these parameters. In terms ofphase-averaged flow statistics, it is found that $\alpha$ primarily controlsthe oscillation amplitude of the streamwise velocity and Reynolds stresses, buthas a negligible impact on their wall-normal structure. On the other hand,$\omega$ determines the size of the region affected by the unsteady forcing,which identifies the so-called Stokes layer thickness $\delta_s$. Within theStokes layer, phase-averaged resolved Reynolds stress profiles featuresubstantial variations during the pulsatile cycle, and the turbulence is out ofequilibrium with the mean flow. Two phenomenological models have been proposedthat capture the influence of flow unsteadiness on $z_0$ and $\delta_s$,respectively.

Mean Flow and Turbulence in Unsteady Canopy Layers