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.

Duke Scholars

Author Gabriel G. Katul Civil and Environmental Engineering