The role of thermal stratification on the co-spectral properties of momentum transport above an Amazonian forest

Abstract The influence of thermal stratification on the turbulent kinetic energy balance has been widely studied; however, its influence on the turbulent stress remains less explored in the presence of tall vegetated canopies and less ideal micrometeorological conditions. Here, the impact of thermal stratification on turbulent momentum flux is considered in the roughness sublayer (RSL) and the atmospheric surface layer (ASL) using the Amazon Tall Tower Observatory (ATTO) in Brazil. A scalewise co-spectral budget (CSB) model is developed using standard closure schemes for the pressure–velocity decorrelation. The CSB revealed that the co-spectrum \$\$ {F}\_{wu}\left({k}\_x\right) \$\$ between longitudinal (\$\$ {u}^{\prime } \$\$) and vertical (\$\$ {w}^{\prime } \$\$) velocity fluctuations is impacted by the energy spectrum of the vertical velocity \$\$ {E}\_{ww}\left({k}\_x\right) \$\$ and the much less studied longitudinal heat-flux co-spectrum \$\$ {F}\_{u{\theta}\_{\mathrm{v}}}\left({k}\_x\right) \$\$, where \$\$ {\theta}\_{\mathrm{v}}^{\prime } \$\$ are temperature fluctuations and \$\$ {k}\_x \$\$ is the longitudinal wavenumber. Under stable, very stable, and dynamic–convective conditions, the scaling exponent in \$\$ {F}\_{wu}\left({k}\_x\right) \$\$ for the inertial subrange (ISR) scales is dominated by \$\$ {F}\_{u{\theta}\_{\mathrm{v}}}\left({k}\_x\right) \$\$ instead of \$\$ {E}\_{ww}\left({k}\_x\right) \$\$. A near \$\$ {k}\_x^{-7/3} \$\$ scaling in \$\$ {F}\_{u{\theta}\_{\mathrm{v}}}\left({k}\_x\right) \$\$ robust to large variations in thermal stratification is found, whereas the Kolmogorov ISR scaling for \$\$ {E}\_{ww}\left({k}\_x\right)\sim {k}\_x^{-5/3} \$\$ is not found. The scale-dependent decorrelation time between \$\$ {u}^{\prime } \$\$ and \$\$ {w}^{\prime } \$\$ is dominated by \$\$ {\epsilon}^{-1/3}{k}\_x^{-2/3} \$\$ in the ISR, but is nearly constant for eddies larger than the vertical velocity integral scale, regardless of stability. Implications of these findings for generalized stability correction functions that are based on the turbulent stress budget instead of the turbulent kinetic energy budget are discussed.