Adjustments to the law of the wall above an Amazon forest explained by a spectral link

Modification to the law of the wall represented by a dimensionless correction function ϕ RSL ( 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 E w w ( k ) (k is the longitudinal wavenumber) and ϕ RSL is then established using a co-spectral budget (CSB) model interpreted by the moving-equilibrium hypothesis. The key finding is that ϕ RSL is determined by the ratio of two turbulent viscosities and is given as ν t , B L / ν t , RSL, where ν t , RSL = ( 1 / A ) ∫ 0 ∞ τ ( k ) E w w ( k ) d k, ν t , B L = k v ( z − d ) u *, τ ( k ) is a scale-dependent decorrelation time scale between velocity components, A = C R / ( 1 − C I ) = 4.5 is predicted from the Rotta constant C R = 1.8, and the isotropization of production constant C I = 3 / 5 given by rapid distortion theory, k v 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 E w w ( k ) and is determined by the turbulent kinetic energy dissipation rate ( ε), the CSB model also predicts that ϕ RSL scales with L B L / L d, where L B L is the length scale of attached eddies to z = d, and L d = u * 3 / ε is a macro-scale dissipation length.