Stratification Effects on Momentum Transfer in the Roughness Sublayer over Tall Forested Canopies

The structure of atmospheric flow in and above the Amazon forest influences a plethora of physical, chemical, and biological processes and is shaped by the interaction between the tall and dense canopy and the drivers of the flow. This interplay challenges classical boundary layer concepts, particularly in non-neutral stratification, where the existence of a well-defined inertial sublayer is difficult to establish in such non-ideal conditions. Observations from the Amazon Tall Tower Observatory (ATTO) indicate that convective structures from the outer layer in unstable stratification and low-frequency submeso motions in stable conditions disrupt the conventional boundary-layer and mixing-layer frameworks. A scale-wise co-spectral budget model is introduced to investigate the vertical velocity spectrum $E_ww(k_x)$ and its link to the vertical momentum transport, where $k_x$ is the longitudinal wavenumber. The model balances mechanical production, pressure decorrelation, and longitudinal buoyancy production (or destruction) in the co-spectral budget for momentum. A key finding is that the momentum flux co-spectrum $F_wu(k_x)$ between longitudinal (u′) and vertical (w′) velocity fluctuations is influenced not only by the vertical velocity energy spectrum but also by the co-spectrum of the longitudinal heat flux $F_uθv(k_x)$, where $θv$ represents temperature fluctuations. Notably, under stable and dynamic-convective conditions, the scaling behavior of $F_wu(k_x)$ is dictated by $F_uθv(k_x)$ when compared to $E_ww(k_x)$. The analysis also reveals a robust $k_x^−7/3$ scaling in $F_uθv(k_x)$ for inertial subrange scales, whereas the classical Kolmogorov $k_x^−5/3$ scaling in $E_ww(k_x)$ is not universally observed. Additionally, the scale-dependent de-correlation time between u′ and w′ follows $ϵ^−1/3kx−2/3$ in the inertial subrange but remains nearly constant for eddies larger than the integral scale of vertical velocity, independent of stability conditions.