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1. Signals of Non-Turbulent Motions Caused by Stable Stratification in Near-Surface Sonic-Anemometer Data

   https://doi.org/10.26208/jy60-kn43  

   Pan, Y; Wray, S C; Patton, E G (January 2024, Penn State Data Commons)

   Understanding the interactions between turbulent and non-turbulent motions has been a persistent challenge faced by the community studying stably stratified turbulent flows. For flows with high Reynolds number, high Rossby number, and stable stratifications, non-turbulent motions share a common characteristic to involve physical mechanisms acting against instability development. Because turbulence is generated through energy cascade via instability development, the presence of non-turbulent motions is expected to modify the energy distribution across scales compared to that of solely turbulent motions. The objective of this work is to identify statistical signals of non-turbulent motions caused by stable stratification. The need to resolve energy-containing motions in both space and time requires high-frequency time series of velocity fluctuations collected using arrays of sonic anemometers. The analysis is performed using data from the Canopy Horizontal Array Turbulence Study (CHATS), during which a total of 31 sonic anemometers were deployed on a horizontal array and on a 30-m tower. Compared to other field campaigns which were also equipped with arrays of sonic anemometers, CHATS took an important advantage of already published nighttime canopy-scale waves derived from aerosol backscatter lidar images. After precluding complexities caused by nonstationarity and horizontal heterogeneity, signals of non-turbulent motions caused by stable stratification are identified from spatial autocorrelations of time-block-averaged velocity fluctuations. These signals agree with existing understanding of turbulent canopy flows and two-dimensional Kelvin-Helmholtz instability development, which predicts a critical wavelength at which motions shift from free instability growth to internal gravity waves. The estimates of critical wavelengths and buoyancy periods agree well with the overall properties of nighttime canopy-scale waves derived from lidar images. 

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2. Stable Boundary Layers and Subfilter-Scale Motions

   https://doi.org/10.3390/atmos14071107  

   McWilliams, James C; Meneveau, Charles; Patton, Edward G; Sullivan, Peter P (July 2023, Atmosphere)

   Recent high-resolution large-eddy simulations (LES) of a stable atmospheric boundary layer (SBL) with mesh sizes N=(5123,10243,20483) or mesh spacings ▵=(0.78,0.39,0.2) m are analyzed. The LES solutions are judged to be converged based on the good collapse of vertical profiles of mean winds, temperature, and low-order turbulence moments, i.e., fluxes and variances, with increasing N. The largest discrepancy is in the stably stratified region above the low-level jet. Subfilter-scale (SFS) motions are extracted from the LES with N=20483 and are compared to sonic anemometer fields from the horizontal array turbulence study (HATS) and its sequel over the ocean (OHATS). The results from the simulation and observations are compared using the dimensionless resolution ratio Λw/▵f where ▵f is the filter width and Λw is a characteristic scale of the energy-containing eddies in vertical velocity. The SFS motions from the observations and LES span the ranges 0.1<Λw/▵f<20 and are in good agreement. The small, medium, and large range of Λw/▵f correspond to Reynolds-averaged Navier–Stokes (RANS), the gray zone (a.k.a. “Terra Incognita”), and fine-resolution LES. The gray zone cuts across the peak in the energy spectrum and then flux parameterizations need to be adaptive and account for partially resolved flux but also “stochastic” flux fluctuations that represent the turbulent correlation between the fluctuating rate of strain and SFS flux tensors. LES data with mesh 20483 will be made available to the research community through the web and tools provided by the Johns Hopkins University Turbulence Database. 

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3. Probing eddy size and its effective mixing length in stably stratified roughness sublayer flows

   https://doi.org/10.1002/qj.4386  

   Peltola, Olli; Aurela, Mika; Launiainen, Samuli; Katul, Gabriel (October 2022, Quarterly Journal of the Royal Meteorological Society)

   Stably stratified roughness sublayer flows are ubiquitous yet remain difficult to represent in models and to interpret using field experiments. Here, continuous high‐frequency potential temperature profiles from the forest floor up to 6.5 times the canopy height observed with distributed temperature sensing (DTS) are used to link eddy topology to roughness sublayer stability correction functions and coupling between air layers within and above the canopy. The experiments are conducted at two forest stands classified as hydrodynamically sparse and dense. Near‐continuous profiles of eddy sizes (length scales) and effective mixing lengths for heat are derived from the observed profiles using a novel conditional sampling approach. The approach utilizes potential temperature isoline fluctuations from a statically stable background state. The transport of potential temperature by an observed eddy is assumed to be conserved (adiabatic movement) and we assume that irreversible heat exchange between the eddy and the surrounding background occurs along the (vertical) periphery of the eddy. This assumption is analogous to Prandtl's mixing‐length concept, where momentum is transported rapidly vertically and then equilibrated with the local mean velocity gradient. A distinct dependence of the derived length scales on background stratification, height above ground, and canopy characteristics emerges from the observed profiles. Implications of these findings for (1) the failure of Monin–Obukhov similarity in the roughness sublayer and (2) above‐canopy flow coupling to the forest floor are examined. The findings have practical applications in terms of analysing similar DTS data sets with the proposed approach, modelling roughness sublayer flows, and interpreting nocturnal eddy covariance measurements above tall forested canopies. 

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4. Wind-Tunnel Experiments of Turbulent Wind Fields over a Two-dimensional (2D) Steep Hill: Effects of the Stable Boundary Layer

   https://doi.org/10.1007/s10546-023-00820-2  

   Zhang, Wei; Markfort, Corey D.; Porté-Agel, Fernando (September 2023, Boundary-Layer Meteorology)

   Flow separation caused by steep topography remains a significant obstacle in accurately predicting turbulent boundary-layer flows over complex terrain, despite the utilization of sophisticated numerical models. The addition of atmospheric thermal stability, in conjunction with steep topography, further complicates the determination of disrupted turbulent wind patterns. The turbulent separated flows over a two-dimensional (2D) steep hill under thermal stratification has not been extensively addressed in previous experimental studies. Such measurements are crucial for enhancing our comprehension of flow physics and validating numerical models. We measured the turbulent wind flows over a 2D steep hill immersed in a stable boundary layer (of the bulk Richardson Number = 0.256) in a thermally-stratified boundary-layer wind tunnel. The flow separation, re-circulation zone and flow reattachment were characterized by the planar particle image velocimetry technique. Vertical profiles of mean air temperature and its fluctuations are also quantified at representative locations above the 2D steep hill and in the near wake region. Results indicate that the separated shear layer, initiated near the crest of the 2D steep hill, dominates the physical process leading to high turbulence levels and the turbulent kinetic energy production in the wake region for both stable and neutral thermal stability. Although the stable boundary layer does not dramatically change the turbulent flow pattern around the hill, the mean separation bubble is elongated by 13%, and its vertical extent is decreased by approximately 20%. Furthermore, the reduced turbulence intensities and turbulent kinetic energy of the near wake flow are attributed to the relatively low turbulence intensity and low momentum of the stable boundary layer due to buoyancy damping, compared to the neutral boundary layer. Additionally, a distinct low-temperature region—a cold pool—is extended beyond the separation bubble, reflecting the significant sheltering effect of the 2D steep hill on the downwind flow and temperature field. 

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5. Statistical state dynamics analysis of buoyancy layer formation via the Phillips mechanism in two-dimensional stratified turbulence

   https://doi.org/10.1017/jfm.2019.72  

   Fitzgerald, Joseph G.; Farrell, Brian F. (April 2019, Journal of Fluid Mechanics)

   Horizontal density layers are commonly observed in stratified turbulence. Recent work (e.g. Taylor & Zhou, J. Fluid Mech. , vol. 823, 2017, R5) has reinvigorated interest in the Phillips instability (PI), by which density layers form via negative diffusion if the turbulent buoyancy flux weakens as stratification increases. Theoretical understanding of PI is incomplete, in part because it remains unclear whether and by what mechanism the flux-gradient relationship for a given example of turbulence has the required negative-diffusion property. Furthermore, the difficulty of analysing the flux-gradient relation in evolving turbulence obscures the operating mechanism when layering is observed. These considerations motivate the search for an example of PI that can be analysed clearly. Here PI is shown to occur in two-dimensional Boussinesq sheared stratified turbulence maintained by stochastic excitation. PI is analysed using the second-order S3T closure of statistical state dynamics, in which the dynamics is written directly for statistical variables of the turbulence. The predictions of S3T are verified using nonlinear simulations. This analysis provides theoretical underpinning of PI based on the fundamental equations of motion that complements previous analyses based on phenomenological models of turbulence. 

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