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Stochastically generated instantaneous velocity profiles are used to reproduce the outer region of rough-wall turbulent boundary layers in a range of Reynolds numbers extending from the wind tunnel to field conditions. Each profile consists in a sequence of steps, defined by the modal velocities and representing uniform momentum zones (UMZs), separated by velocity jumps representing the internal shear layers. Height-dependent UMZ is described by a minimal set of attributes: thickness, mid-height elevation, and streamwise (modal) and vertical velocities. These are informed by experimental observations and reproducing the statistical behaviour of rough-wall turbulence and attached eddy scaling, consistent with the corresponding experimental datasets. Sets of independently generated profiles are reorganized in the streamwise direction to form a spatially consistent modal velocity field, starting from any randomly selected profile. The operation allows one to stretch or compress the velocity field in space, increases the size of the domain and adjusts the size of the largest emerging structures to the Reynolds number of the simulated flow. By imposing the autocorrelation function of the modal velocity field to be anchored on the experimental measurements, we obtain a physically based spatial resolution, which is employed in the computation of the velocity spectrum, and second-order structure functions. The results reproduce the Kolmogorov inertial range extending from the UMZ and their attached-eddy vertical organization to the very-large-scale motions (VLSMs) introduced with the reordering process. The dynamic role of VLSM is confirmed in the$$-u^{\prime }w^{\prime }$$co-spectra and in their vertical derivative, representing a scale-dependent pressure gradient contribution. 

The statistical properties of uniform momentum zones (UMZs) are extracted from laboratory and field measurements in rough wall turbulent boundary layers to formulate a set of stochastic models for the simulation of instantaneous velocity profiles. A spatiotemporally resolved velocity dataset, covering a field of view of$$8 \times 9\,{\rm m}^2$$, was obtained in the atmospheric surface layer using super-large-scale particle image velocimetry (SLPIV), as part of the Grand-scale Atmospheric Imaging Apparatus (GAIA). Wind tunnel data from a previous study are included for comparison (Heiselet al.,J. Fluid Mech., vol. 887, 2020, R1). The probability density function of UMZ attributes such as their thickness, modal velocity and averaged vertical velocity are built at varying elevations and modelled using log-normal and Gaussian distributions. Inverse transform sampling of the distributions is used to generate synthetic step-like velocity profiles that are spatially and temporally uncorrelated. Results show that in the wide range of wall-normal distances and$$Re_\tau$$up to$$\sim O(10^6)$$investigated here, shear velocity scaling is manifested in the velocity jump across shear interfaces between adjacent UMZs, and attached eddy behaviour is observed in the linear proportionality between UMZ thickness and their wall normal location. These very same characteristics are recovered in the generated instantaneous profiles, using both fully stochastic and data-driven hybrid stochastic (DHS) models, which address, in different ways, the coupling between modal velocities and UMZ thickness. Our method provides a stochastic approach for generating an ensemble of instantaneous velocity profiles, consistent with the structural organisation of UMZs, where the ensemble reproduces the logarithmic mean velocity profile and recovers significant portions of the Reynolds stresses and, thus, of the streamwise and vertical velocity variability. 

Abstract Understanding the organization and dynamics of turbulence structures in the atmospheric surface layer (ASL) is important for fundamental and applied research in different fields, including weather prediction, snow settling, particle and pollutant transport, and wind energy. The main challenges associated with probing and modeling turbulence in the ASL are: i) the broad range of turbulent scales associated with the different eddies present in high Reynolds-number boundary layers ranging from the viscous scale (𝒪(mm)) up to large energy-containing structures (𝒪(km)); ii) the non-stationarity of the wind conditions and the variability associated with the daily cycle of the atmospheric stability; iii) the interactions among eddies of different sizes populating different layers of the ASL, which contribute to momentum, energy, and scalar turbulent fluxes. Creative and innovative measurement techniques are required to probe near-surface turbulence by generating spatio-temporally-resolved data in the proximity of the ground and, at the same time, covering the entire ASL height with large enough streamwise extent to characterize the dynamics of larger eddies evolving aloft. To this aim, the U.S. National Science Foundation sponsored the development of the Grand-scale Atmospheric Imaging Apparatus (GAIA) enabling super-large snow particle image velocimetry (SLPIV) in the near-surface region of the ASL. This inaugural version of GAIA provides a comprehensive measuring system by coupling SLPIV and two scanning Doppler LiDARs to probe the ASL at an unprecedented resolution. A field campaign performed in 2021–2022 and its preliminary results are presented herein elucidating new research opportunities enabled by the GAIA measuring system.