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Modification to the law of the wall represented by a dimensionless correction function ϕRSL(z/h) is derived using atmospheric turbulence measurements collected at two sites in the Amazon in near-neutral stratification, where z is the distance from the forest floor and h is the mean canopy height. The sites are the Amazon Tall Tower Observatory for z/h∈[1,2.3] and the Green Ocean Amazon (GoAmazon) site for z/h∈[1,1.4]. A link between the vertical velocity spectrum Eww(k) (k is the longitudinal wavenumber) and ϕRSL is then established using a co-spectral budget (CSB) model interpreted by the moving-equilibrium hypothesis. The key finding is that ϕRSL is determined by the ratio of two turbulent viscosities and is given as νt,BL/νt,RSL, where νt,RSL=(1/A)∫0∞τ(k)Eww(k)dk, νt,BL=kv(z−d)u*, τ(k) is a scale-dependent decorrelation time scale between velocity components, A=CR/(1−CI)=4.5 is predicted from the Rotta constant CR=1.8, and the isotropization of production constant CI=3/5 given by rapid distortion theory, kv is the von Kármán constant, u* is the friction velocity at the canopy top, and d is the zero-plane displacement. Because the transfer of energy across scales is conserved in Eww(k) and is determined by the turbulent kinetic energy dissipation rate (ε), the CSB model also predicts that ϕRSL scales with LBL/Ld, where LBL is the length scale of attached eddies to z=d, and Ld=u*3/ε is a macro-scale dissipation length.
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This content will become publicly available on October 1, 2026
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 between longitudinal () and vertical () velocity fluctuations is impacted by the energy spectrum of the vertical velocity and the much less studied longitudinal heat‐flux co‐spectrum , where are temperature fluctuations and is the longitudinal wavenumber. Under stable, very stable, and dynamic–convective conditions, the scaling exponent in for the inertial subrange (ISR) scales is dominated by instead of . A near scaling in robust to large variations in thermal stratification is found, whereas the Kolmogorov ISR scaling for is not found. The scale‐dependent decorrelation time between and is dominated by 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.
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- Award ID(s):
- 2028633
- PAR ID:
- 10651510
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Quarterly Journal of the Royal Meteorological Society
- Volume:
- 151
- Issue:
- 772
- ISSN:
- 0035-9009
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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