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 Phi(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 is an element of [1, 2.3] and the Green Ocean Amazon (GoAmazon) site for z/h is an element of [1, 1.4]. A link between the vertical velocity spectrum E-ww(k) (k is the longitudinal wavenumber) and Phi(RSL) is then established using a co-spectral budget (CSB) model interpreted by the moving-equilibrium hypothesis. The key finding is that /RSL is determined by the ratio of two turbulent viscosities and is given as v(t,BL)/v(t,RSL), where v(t,RSL) = (1/A) integral(infinity)(0) tau(k)E-ww(k)dk, v(t,BL) = k(v)(z- d)u,,, tau(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 Karman 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-ww(k) and is determined by the turbulent kinetic energy dissipation rate (epsilon), the CSB model also predicts that Phi(RSL) scales with L-BL/L-d, where L-BL is the length scale of attached eddies to z = d, and L-d = u(+)(3)/epsilon is a macro-scale dissipation length.