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A number of recent studies have demonstrated the existence of so-called large- and very-large-scale motions (LSM, VLSM) that occur in the logarithmic region of inertia-dominated wall-bounded turbulent flows. These regions exhibit significant streamwise coherence, and have been shown to modulate the amplitude and frequency of small-scale inner-layer fluctuations in smooth-wall turbulent boundary layers. In contrast, the extent to which analogous modulation occurs in inertia-dominated flows subjected to convective thermal stratification (low Richardson number) and Coriolis forcing (low Rossby number), has not been considered. And yet, these parameter values encompass a wide range of important environmental flows. In this article, we present evidence of amplitude modulation (AM) phenomena in the unstably stratified (i.e. convective) atmospheric boundary layer, and link changes in AM to changes in the topology of coherent structures with increasing instability. We perform a suite of large eddy simulations spanning weakly ($-z_{i}/L=3.1$) to highly convective ($-z_{i}/L=1082$) conditions (where$-z_{i}/L$is the bulk stability parameter formed from the boundary-layer depth$z_{i}$and the Obukhov length $L$) to investigate how AM is affected by buoyancy. Results demonstrate that as unstable stratification increases, the inclination angle of surface layer structures (as determined from the two-point correlation of streamwise velocity) increases from$\unicode[STIX]{x1D6FE}\approx 15^{\circ }$for weakly convective conditions to nearly vertical for highly convective conditions. As$-z_{i}/L$increases, LSMs in the streamwise velocity field transition from long, linear updrafts (or horizontal convective rolls) to open cellular patterns, analogous to turbulent Rayleigh–Bénard convection. These changes in the instantaneous velocity field are accompanied by a shift in the outer peak in the streamwise and vertical velocity spectra to smaller dimensionless wavelengths until the energy is concentrated at a single peak. The decoupling procedure proposed by Mathiset al.(J. Fluid Mech., vol. 628, 2009a, pp. 311–337) is used to investigate the extent to which amplitude modulation of small-scale turbulence occurs due to large-scale streamwise and vertical velocity fluctuations. As the spatial attributes of flow structures change from streamwise to vertically dominated, modulation by the large-scale streamwise velocity decreases monotonically. However, the modulating influence of the large-scale vertical velocity remains significant across the stability range considered. We report, finally, that amplitude modulation correlations are insensitive to the computational mesh resolution for flows forced by shear, buoyancy and Coriolis accelerations.

Within the diabatic atmospheric surface layer (ASL) under quasi-stationary and horizontal homogeneous conditions, the mean velocity profile deviates from its conventional logarithmic shape by a height-dependent universal stability correction function ϕm(ζ) that varies with the stability parameter ζ. The ζ parameter measures the relative importance of mechanical to buoyant production or destruction of turbulent kinetic energy (TKE) within the ASL. A link between ϕm(ζ) and the spectrum of turbulence in the ASL was recently proposed by Katul et al. [“Mean velocity profile in a sheared and thermally stratified atmospheric boundary layer,” Phys. Rev. Lett. 107, 268502 (2011)]. By accounting for the stability-dependence of TKE production, Katul et al. were able to recover scalings for ϕm with the anticipated power-law exponents for free convective, slightly unstable, and stable conditions. To obtain coefficients for the ϕm(ζ) curve in good agreement with empirical formulas, they introduced a correction for the variation of the integral lengthscale of vertical velocity with ζ estimated from the Kansas experiment. In the current work, the link between the coefficients in empirical curves for ϕm(ζ) and stability-dependent properties of turbulence in the ASL, including the variation with ζ of the integral lengthscale and the anisotropy of momentum transporting eddies is investigated using data from the Advection Horizontal Array Turbulence Study. The theoretical framework presented by Katul et al. is revised to account explicitly for these effects. It is found that the coefficients in the ϕm(ζ) curve for unstable and near-neutral conditions can be explained by accounting for the stability-dependence of the integral lengthscale and anisotropy of momentum-transporting eddies; however, an explanation for the observed ϕm(ζ) curve for stable conditions remains elusive. The effect of buoyancy on the horizontal and vertical integral lengthscales is also analyzed in detail.

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A spatially local decomposition of turbulent fluxes based on properties of spatial filters is used to develop a new method of estimating random error in turbulent moments of any order. The proposed error estimation method does not require an estimate of the integral time scale, which can be highly sensitive to the method used to calculate it. The error estimation method is validated using synthetic flux data with a known ensemble mean and intercompared with existing methods using data from the Advection Horizontal Array Turbulence Study (AHATS). Typical errors for a 27.3-min block of data collected at a height of 8 m are found to be approximately 10% for the heat flux and 7-15% for variances. The error in the momentum flux increases rapidly with increasing atmospheric instability, reaching values of 40% or greater for unstable conditions. A new method based on filtering is also proposed to estimate integral time scales of turbulent quantities.