Abstract.The memory timescale that characterizes root-zone soil mois-

The low-wavenumber regime of the spectrum of turbulence commensurate with Townsend’s “attached” eddies is investigated here for the near-neutral atmospheric surface layer (ASL) and the roughness sublayer (RSL) above vegetation canopies. The central thesis corroborates the significance of the imbalance between local production and dissipation of turbulence kinetic energy (TKE) and canopy shear in challenging the classical distance-from-the-wall scaling of canonical turbulent boundary layers. Using five experimental datasets (two vegetation canopy RSL flows, two ASL flows, and one open-channel experiment), this paper explores (i) the existence of a low-wavenumber k−1 scaling law in the (wind) velocity spectra or, equivalently, a logarithmic scaling ln(r) in the velocity structure functions; (ii) phenomenological aspects of these anisotropic scales as a departure from homogeneous and isotropic scales; and (iii) the collapse of experimental data when plotted with different similarity coordinates. The results show that the extent of the k−1 and/or ln(r) scaling for the longitudinal velocity is shorter in the RSL above canopies than in the ASL because of smaller scale separation in the former. Conversely, these scaling laws are absent in the vertical velocity spectra except at large distances from the wall. The analysis reveals that the statistics of the velocity differences Δu and Δw approach a Gaussian-like behavior at large scales and that these eddies are responsible for momentum/energy production corroborated by large positive (negative) excursions in Δu accompanied by negative (positive) ones in Δw. A length scale based on TKE dissipation collapses the velocity structure functions at different heights better than the inertial length scale.

The inadequacy of conventional gradient diffusion in closure modelling of turbulent heat fluxes within the convective atmospheric boundary layer is often alleviated by accounting for non-local transport effects, such as Deardorff's counter-gradient models, Wyngaard's transport asymmetry closures or mass-flux parametrization. This concept of large-eddy flux transport is examined here with the principal aim of unifying these seemingly different models. Using large-eddy simulation (LES) runs for the atmospheric boundary layer, spanning weakly to strongly convective conditions, a generic diagnostic framework that encodes the role of third-order moments in non-local transport is developed and tested. The premise is that these non-local effects are responsible for the inherent asymmetry in vertical transport and hence the necessary non-Gaussian nature of the joint probability density function (JPDF) of vertical velocity and potential temperature must account for these effects. Conditional sampling (quadrant analysis) of this JPDF and the imbalance between the flow mechanisms of ejections and sweeps are used to characterize this asymmetry, which is then linked to the third-order moments using a cumulant-discard method for the Gram-Charlier expansion of the JPDF. While the concept of ejection-sweep events used here is not a simple extension of that commonly used in the surface layer, their connection to third-order moments shows that the concepts of bottom-up/top-down diffusion or updraught/downdraught models are accounted for by various quadrants of the JPDF. An analogy between mass-flux models and the relaxed eddy accumulation method reveals that there is a seemingly implicit assumption of a Gaussian JPDF in the former.

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