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NASA NTRSDate not supplied

Sensitivity to Snapshot Frequency in the POD-Based Reduced-Order Modeling of Flow over a Gaussian Bump

The flow over a Gaussian bump at a Reynolds number of 10^6, based on the bump length and freestream conditions, and a Mach number of 0.2, was simulated using wall-modeled large eddy simulation (WMLES). The incoming turbulent flow exhibits relaminarization upstream of the bump apex, due to the favourable pressure gradient acceleration induced by the bump curvature, as well as separation, reattachment and a detached shear layer downstream of the apex. A Galerkin reduced-order model (ROM) was then constructed using a proper orthogonal decomposition (POD) modal basis. The complex, three-dimensional flow features are captured by spatial POD modes differently based on the frequency of the high-fidelity snapshots originally provided. POD modes constructed from differently sampled snapshot matrices were then truncated to retain 90% of the turbulence kinetic energy in the domain of interest. A parametric study is conducted to evaluate the effect of the frequency of snapshots used to construct the POD-ROM.

turbulence↗

DOE OSTI2025

Computational diagnostics and characterization of combustion recession in diesel sprays

While low-temperature combustion (LTC) strategies have been found to mitigate nitrogen oxides and particulate matter emissions in diesel engines, studies have also associated LTC with an increase in unburnt hydrocarbons. With more recent studies on diesel after end-of-injection (AEOI), combustion recession is identified as a phenomenon where at near nozzle region, high-temperature ignition (HTI) combustion can propagate back to the nozzle tip consuming the unburnt hydrocarbons AEOI. Current literature has suggested that combustion recession is controlled by auto-ignition. However, high-fidelity simulations and detailed analysis of such a mechanism are missing. In this study, comprehensive Large Eddy Simulations of a reacting spray at “Spray A” conditions are performed, where detailed analysis of combustion recession concerning flame morphology and propagation modes are included. In particular, this study demonstrated for the first time that while combustion recession is mainly auto-ignition dominated (consistent with the literature), a cool flame was found to deflagrate towards the richer regions of the mixture, promoting mixing and increasing the mixture temperature. This leads to HTI kernels, which then grow and develop as deflagrative waves, therefore sustaining the combustion recession process. The study also detailed the extinction mechanism of combustion: the entrainment wave will overlean the near-nozzle mixtures, rendering it unable to support HTI, which leads to the extinction of the upstream flame AEOI in lower reactivity mixtures. Combustion recession is also observed to be contingent on the chemical and diffusion processes, even at low scalar dissipation rates. Finally, a new criterion for combustion recession based on chemical explosive mode is proposed and validated with previous combustion recession index to quantify the extent of HTI in near-nozzle mixtures AEOI. The newly developed metric combined with a previous experimentally-based metric can provide simple but valuable measurements of the degree and propensity of the upstream flame AEOI.

CEMA↗

DOE OSTI2019

Simulation of Mesoscale Cellular Convection in Marine Stratocumulus: 2. Nondrizzling Conditions

This is the second of two large-eddy simulation studies on the mechanisms of mesoscale cellular organization in drizzling (open cells) and nondrizzling marine stratocumulus (closed cells). This study uses a hard nudging approach which maintains fixed horizontal-mean temperature and humidity profiles for a well-mixed boundary layer with a constant boundary layer depth. For the case studied, closed cells develop and broaden by 32 hr to an aspect ratio of 25. Simulations show that the closed-cell mesoscale cellular convection is driven by positive feedback from cloud-induced mesoscale perturbations of longwave radiative cooling. A conceptual model for closed-cell stratocumulus as a mesoscale wavelength hydrodynamic instability in which mesoscale moist and dry anomalies spontaneously grow is presented. In simulations in which long-wavelength sinusoidal moisture anomalies are initially imposed, these anomalies evolve into amplifying closed cells. The cell structure is visualized with a compositing approach based on sorting grid columns by their mesoscale-smoothed total water path. A thermally direct mesoscale circulation pattern develops in the interior of the boundary layer with buoyant mesoscale updrafts, thicker cloud, and a slightly higher capping inversion in the moister columns. There is a mesoscale flow of above-inversion air down the slightly sloping capping inversion from the moist to the dry regions, reinforced by cloud top radiative cooling. This strengthens the mesoscale anomalies by preferentially cooling and drying the already dry regions. The sloping inversion flow is not driven as efficiently if the radiative cooling is artificially horizontally homogenized, partly disrupting this positive feedback and the resulting closed-cell development.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2018

The effect of artificial bulk viscosity in simulations of forced compressible turbulence

The use of an artificial bulk viscosity for shock stabilization is a common approach employed in turbulence simulations with high-order numerics. The effect of the artificial bulk viscosity is analyzed in the context of large eddy simulations by using as a test case simulations of linearly-forced compressible homogeneous turbulence (Petersen and Livescu, 2010 [12]). This case is unique in that it allows for the specification of a priori target values for total dissipation and ratio of solenoidal to dilatational dissipation. A comparison between these target values and the true predicted levels of dissipation is thus used to investigate the performance of the artificial bulk viscosity. Results show that the artificial bulk viscosity is effective at achieving stable solutions, but also leads to large values of artificial dissipation that outweigh the physical dissipation caused by fluid viscosity. An alternate approach, which employs the artificial thermal conductivity only, shows that the dissipation of dilatational modes is entirely due to the fluid viscosity. However, this method leads to unwanted Gibbs oscillations around the shocklets. The use of shock sensors that further localize the artificial bulk viscosity did not reduce the amount of artificial dissipation introduced by the artificial bulk viscosity. Finally, an improved forcing function that explicitly accounts for the role of the artificial bulk viscosity in the budget of turbulent kinetic energy was explored.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Numerical Simulation of Metal Melt Flow in a One-Strand Tundish Regarding Active Filtration and Reactive Cleaning

In the paper, two different cleaning strategies for nonmetallic inclusions in steel melts, active filtration and reactive cleaning, are examined in a prototype tundish configuration. In active filtration, nonmetallic inclusions are deposited at the filter surfaces. In reactive cleaning, nonmetallic inclusions stick to the filter surfaces, too. In addition, they are floated by the action of carbon monoxide bubbles, which are generated by reaction between carbon and oxygen in the steel melt. In order to compare the performance of both strategies, numerical simulations of the two-phase flows of steel melt and dispersed nonmetallic inclusions are performed. Turbulence is resolved with implicit large eddy simulation. If necessary, species transports of dissolved carbon in the melt and reaction with oxygen are employed. Cleaning efficiencies are deduced from the simulations which demonstrate that reactive cleaning is much more efficient than active filtration.

36 MATERIALS SCIENCE↗

DOE OSTI2022

“Gray Zone” Simulations Using a Three-Dimensional Planetary Boundary Layer Parameterization in the Weather Research and Forecasting Model

Abstract Generating accurate weather forecasts of planetary boundary layer (PBL) properties is challenging in many geographical regions, oftentimes due to complex topography or horizontal variability in, for example, land characteristics. While recent advances in high-performance computing platforms have led to an increase in the spatial resolution of numerical weather prediction (NWP) models, the horizontal gridcell spacing (Δ x ) of many regional-scale NWP models currently fall within or are beginning to approach the gray zone (i.e., Δ x ≈ 100–1000 m). At these gridcell spacings, three-dimensional (3D) effects are important, as the most energetic turbulent eddies are neither fully parameterized (as in traditional mesoscale simulations) nor fully resolved [as in traditional large-eddy simulations (LES)]. In light of this modeling challenge, we have implemented a 3D PBL parameterization for high-resolution mesoscale simulations using the Weather Research and Forecasting Model. The PBL scheme, which is based on the algebraic model developed by Mellor and Yamada, accounts for the 3D effects of turbulence by calculating explicitly the momentum, heat, and moisture flux divergences in addition to the turbulent kinetic energy. In this study, we present results from idealized simulations in the gray zone that illustrate the benefit of using a fully consistent turbulence closure framework under convective conditions. While the 3D PBL scheme reproduces the evolution of convective features more appropriately than the traditional 1D PBL scheme, we highlight the need to improve the turbulent length scale formulation. Significance Statement The spatial resolution of weather models continues to increase at a rapid rate in accordance with the enhancement of computing power. As a result, smaller-scale atmospheric features become more explicitly resolved. However, most numerical models still ignore the impact of horizontal weather variations on boundary layer flows, which becomes more important at these smaller spatial scales. To address this issue, we have implemented a new modeling approach, using fundamental principles, which accounts for horizontal variability. Our results show that including three-dimensional effects of turbulence is necessary to achieve realistic boundary layer characteristics. This novel technique may be useful for many applications including complex terrain flows, pollutant dispersion, and surface–atmosphere interaction studies.

Juliano, Timothy W.↗

DOE OSTI2026

An uncertainty visualization framework for large-scale cardiovascular flow simulations: A case study on aortic stenosis

We present a generalizable uncertainty quantification (UQ) and visualization framework for lattice Boltzmann method simulations of high Reynolds number vascular flows, demonstrated on a patient-specific stenosed aorta. The framework combines EasyVVUQ for parameter sampling with large-eddy simulation turbulence modeling in HemeLB, and executes ensembles on the Frontier exascale supercomputer. Spatially resolved metrics, including entropy and isosurface-crossing probability, are used to map uncertainty in pressure and wall shear stress fields directly onto vascular geometries. Two sources of model variability are examined: inlet peak velocity and the Smagorinsky constant. Inlet velocity variation produces high uncertainty downstream of the stenosis where turbulence develops, while upstream regions remain stable. Smagorinsky constant variation has little effect on the large-scale pressure field but increases WSS uncertainty in localized high-shear regions. In both cases, the stenotic throat manifests low entropy, indicative of robust identification of elevated WSS. By linking quantitative UQ measures to three-dimensional anatomy, the framework improves interpretability over conventional 1D UQ plots and supports clinically relevant decision-making, with broad applicability to vascular flow problems requiring both accuracy and spatial insight.

Hemodynamics↗

DOE OSTI2019

Explicit Filtering and Reconstruction to Reduce Grid Dependence in Convective Boundary Layer Simulations Using WRF-LES

As model grid resolutions move from the mesoscale to the microscale, turbulent structures represented in atmospheric boundary layer simulations change dramatically. At intermediate resolutions, the so-called gray zone, turbulent motions are not resolved accurately, posing a challenge to numerical simulations. The representation of turbulence is also highly sensitive to the choice of closure model. Here, we examine explicit filtering and reconstruction in the gray zone as a technique to better represent atmospheric turbulence. The convective boundary layer is simulated using the Weather Research and Forecasting (WRF) Model with horizontal resolutions ranging from 25 m to 1 km. Four large-eddy simulation (LES) turbulence models are considered: the Smagorinsky model, the TKE-1.5 model, and two versions of the dynamic reconstruction model (DRM). The models are evaluated by their ability to produce consistent mean potential temperature profiles, heat and momentum fluxes, velocity fields, and turbulent kinetic energy spectra as the grids become coarser. The DRM, a mixed model that uses an explicit filtering and reconstruction technique to account for resolvable subfilter-scale (RSFS) stresses, performs very well at resolutions of 500 m and 1 km without any special tuning, whereas the Smagorinsky and TKE-1.5 models produce heavily grid-dependent results.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Equipping Neural Network Surrogates with Uncertainty for Propagation in Physical Systems

Coarse-grained or filtered models typically rely on closure models to account for unresolved scales. For instance, large eddy simulation for modeling turbulent fluid flows explicitly resolves the largest scales, but requires modeling closure terms to account for the sub-filter scales. With the vast amount of data available from high-fidelity simulations, there are unique opportunities to leverage data-driven modeling techniques to formulate expressive and flexible closure models. Despite their flexibility, data-driven models struggle in domain shift settings, i.e. when deployed in configurations not captured in the training dataset. In particular, the efficacy of neural network surrogates is difficult to assess a priori due to the deterministic, point-estimate nature of predictions. In high-consequence applications, such models require reliable uncertainty estimates in the data-informed and out-of-distribution regimes. To quantify uncertainties in both regimes, we employ Bayesian neural networks which are able to capture both epistemic and aleatoric uncertainties. We will discuss challenges associated with the training and evaluation of these networks. Furthermore, we will discuss uncertainty embedding strategies to enable efficient sampling and propagation of uncertainty through high-fidelity simulations.

Bayesian neural networks↗

NASA NTRSDate not supplied

Wall-modeled LES of the Three-dimensional Speed Bump Experiment

We evaluate the performance of wall-modeled large eddy simulation (WMLES) in predicting smooth-body turbulent flow separation for a three-dimensional Gaussian-shaped speed bump geometry. The Reynolds number based on the bump length is 2 million, and an unstructured compressible finite-volume solver is used with an equilibrium wall model and dynamic subgrid scale model. Spanwise periodic simulations of the centerline two-dimensional bump were used to assess grid resolution requirements, and resolving the thin internal layer in the accelerating region was found to be necessary to correctly capture the downstream separated flow region. Based on these insights, an optimized grid that was smaller by a factor of two provided comparable accuracy to a finer grid that has been used by us and other researchers in past studies. Using insights gained from the spanwise periodic simulation, an unstructured polyhderal grid with about 250 million cells was used for the three-dimensional (3D) configuration with inviscid tunnel side and top walls. Detailed comparisons of wall skin-friction coefficient, wall pressure, velocity and turbulent stresses with available experimental data indicated excellent agreement. While the low-Reynolds Number Spalart-Allmaras RANS model with rotation/curvature correction gave qualitatively good agreement with experiments, WMLES showed significantly more accurate quantitative predictions of the flowfield. The 3D WMLES showed good agreement with experiments in the separated region, and the centerplane results indicated a different separation topology compared to the spanwise periodic simulation.

Computational Fluid Dynamics↗

DOE OSTI2021

Scaling of Turbulent Viscosity and Resistivity: Extracting a Scale-dependent Turbulent Magnetic Prandtl Number

Turbulent viscosity νt and resistivity ηt are perhaps the simplest models for turbulent transport of angular momentum and magnetic fields, respectively. The associated turbulent magnetic Prandtl number Pr t ≡ ν t /η t has been well recognized to determine the final magnetic configuration of accretion disks. Here, we present an approach to determining these "effective transport" coefficients acting at different length scales using coarse-graining and recent results on decoupled kinetic and magnetic energy cascades. By analyzing the kinetic and magnetic energy cascades from a suite of high-resolution simulations, we show that our definitions of ν t , η t , and Pr t have power-law scalings in the "decoupled range." We observe that Pr t ≈ 1–2 at the smallest inertial-inductive scales, increasing to ≈5 at the largest scales. Furthermore, based on physical considerations, our analysis suggests that Pr t has to become scale independent and of order unity in the decoupled range at sufficiently high Reynolds numbers (or grid resolution) and that the power-law scaling exponents of velocity and magnetic spectra become equal. In addition to implications for astrophysical systems, the scale-dependent turbulent transport coefficients offer a guide for large-eddy simulation modeling.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRSDate not supplied

Turbulent Simulations of Cooling Jets in Crossflow

Turbulent flow simulations were completed of the THX-III single hole film cooling experiment performed at NASA Glenn Research Center (GRC). Two different Large-Eddy Simulation (LES) approaches were completed along with a RANS based study. The first LES approach utilizes the Flux Reconstruction (FR) based finite element code GFR, while the second approach makes use of the compact difference solver FDL3DI. Both LES codes were run on grids larger than 1.5 Billion degrees of freedom (DoF). The RANS simulations used FUN3D and included a grid convergence as a turbulence closure study. A summary of the computational approaches and key findings are presented along with the experimental measurements. Significant progress has been made towards the completion of this work, as all but one simulation have been completed. The preliminary findings have shown the LES approaches have excellent agreement with each other, and closely follow the trends of the experiment. The Reynolds stress RANS closure, while the best of the RANS results, had difficulty matching the results of the LES and experimental measurements.

High-Order Methods↗

NASA NTRS2018

Comparisons of Bispectral and Polarimetric Retrievals of Marine Boundary Layer Cloud Microphysics: Case Studies Using a LES- Satellite Retrieval Simulator

Many passive remote-sensing techniques have been developed to retrieve cloud microphysical properties from satellite-based sensors, with the most common approaches being the bispectral and polarimetric techniques. These two vastly different retrieval techniques have been implemented for a variety of polar-orbiting and geostationary satellite platforms, providing global climatological data sets. Prior instrument comparison studies have shown that there are systematic differences between the droplet size retrieval products (effective radius) of bispectral (e.g., MODIS, Moderate Resolution Imaging Spectroradiometer) and polarimetric (e.g., POLDER, Polarization and Directionality of Earth's Reflectances) instruments. However, intercomparisons of airborne bispectral and polarimetric instruments have yielded results that do not appear to be systematically biased relative to one another. Diagnosing this discrepancy is complicated, because it is often difficult for instrument intercomparison studies to isolate differences between retrieval technique sensitivities and specific instrumental differences such as calibration and atmospheric correction. In addition to these technical differences the polarimetric retrieval is also sensitive to the dispersion of the droplet size distribution (effective variance), which could influence the interpretation of the droplet size retrieval. To avoid these instrument-dependent complications, this study makes use of a cloud remote-sensing retrieval simulator. Created by coupling a large-eddy simulation (LES) cloud model with a 1-D radiative transfer model, the simulator serves as a test bed for understanding differences between bispectral and polarimetric retrievals. With the help of this simulator we can not only compare the two techniques to one another (retrieval intercomparison) but also validate retrievals directly against the LES cloud properties. Using the satellite retrieval simulator, we are able to verify that at high spatial resolution (50m) the bispectral and polarimetric retrievals are highly correlated with one another within expected observational uncertainties. The relatively small systematic biases at high spatial resolution can be attributed to different sensitivity limitations of the two retrievals. In contrast, a systematic difference between the two retrievals emerges at coarser resolution. This bias largely stems from differences related to sensitivity of the two retrievals to unresolved inhomogeneities in effective variance and optical thickness. The influence of coarse angular resolution is found to increase uncertainty in the polarimetric retrieval but generally maintains a constant mean value.

Miller, Daniel J.↗

NASA NTRS2018

Comparisons of Bispectral and Polarimetric Retrievals of Marine Boundary Layer Cloud Microphysics: Case Studies Using a LES-Satellite Retrieval Simulator

Many passive remote-sensing techniques have been developed to retrieve cloud microphysical properties from satellite-based sensors, with the most common approaches being the bispectral and polarimetric techniques. These two vastly different retrieval techniques have been implemented for a variety of polar-orbiting and geostationary satellite platforms, providing global climatological data sets. Prior instrument comparison studies have shown that there are systematic differences between the droplet size retrieval products (effective radius) of bispectral (e.g., MODIS, Moderate Resolution Imaging Spectroradiometer) and polarimetric (e.g., POLDER, Polarization and Directionality of Earth's Reflectances) instruments. However, intercomparisons of airborne bispectral and polarimetric instruments have yielded results that do not appear to be systematically biased relative to one another. Diagnosing this discrepancy is complicated, because it is often difficult for instrument intercomparison studies to isolate differences between retrieval technique sensitivities and specific instrumental differences such as calibration and atmospheric correction. In addition to these technical differences the polarimetric retrieval is also sensitive to the dispersion of the droplet size distribution (effective variance), which could influence the interpretation of the droplet size retrieval. To avoid these instrument-dependent complications, this study makes use of a cloud remote-sensing retrieval simulator. Created by coupling a large-eddy simulation (LES) cloud model with a 1-D radiative transfer model, the simulator serves as a test bed for understanding differences between bispectral and polarimetric retrievals. With the help of this simulator we can not only compare the two techniques to one another (retrieval intercomparison) but also validate retrievals directly against the LES cloud properties. Using the satellite retrieval simulator, we are able to verify that at high spatial resolution (50 m) the bispectral and polarimetric retrievals are highly correlated with one another within expected observational uncertainties. The relatively small systematic biases at high spatial resolution can be attributed to different sensitivity limitations of the two retrievals. In contrast, a systematic difference between the two retrievals emerges at coarser resolution. This bias largely stems from differences related to sensitivity of the two retrievals to unresolved inhomogeneities in effective variance and optical thickness. The influence of coarse angular resolution is found to increase uncertainty in the polarimetric retrieval but generally maintains a constant mean value.

Miller, Daniel J.↗

DOE OSTI2022

Lifting Condensation Level Height (LCL Height) Value-Added Product Report

The lifting condensation level height (LCL, m) is determined from continuous surface-air observations of relative humidity and temperature as the altitude where the surface-air moisture equals saturation following a dry-adiabatic ascent. Values are computed from surface meteorological observations for 16 facilities belonging to the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility Southern Great Plains (SGP) atmospheric observatory and for 133 Oklahoma Mesonet (OKM) stations. The LCL Height Value-Added Product (VAP) was developed for use by the Large-Eddy Simulation (LES) ARM Symbiotic Simulation and Observation (LASSO) project (Gustafson et al. 2016, 2017, 2018, 2020).

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Quantifying vertical wind shear effects in shallow cumulus clouds over Amazonia

Abstract. This study analyses and quantifies the effects of vertical wind shear (VWS) on the properties of shallow cumulus cloud fields over Central Amazonia. We perform idealised simulations with high resolution (50 m horizontally and 20 m vertically) using the Dutch Atmospheric Large-Eddy Simulation (DALES) model, changing the initial conditions and large-scale forcing of VWS. The resulting cloud field is analysed by applying a cloud tracking algorithm to generate Lagrangian datasets of the life cycle of individual clouds as well as their time-varying core and margin dimensions. The reference run has no wind speed or directional shear and represents a typical day in the local dry season. Numerical experiments with moderate and high wind speed shear are simulated by adding linear increases in the wind speed of 1.2 and 2.4 m s−1 km−1, respectively. Three additional runs are made by adding 90∘ of wind rotation between the surface and the top of the domain (5 km) on top of the three wind speed shear conditions. We find that clouds developing in a sheared environment have horizontal equivalent diameter increased by up to 100 m on average, but the cloud depth is reduced. Our quantification shows that VWS tends to increase the size of the cloud cores but reduces their relative area, volume, and mass fractions compared to the overall cloud dimensions. The addition of 2.4 m s−1 km−1 of VWS decreases the relative core area by about 0.03 (about 10 % of the overall average) and its volume and mass ratios by about 0.05 (10 %–25 % in relative terms). Relevant for the cloud transport properties is that the updraught speed and the liquid water content are lower within the cores, and consequently so is the upward mass flux. All quantifications of mean cloud properties point to the inhibition of convective strength by VWS, therefore hampering the shallow-to-deep transition. However, open questions still remain given that the individually deepest clouds were simulated under high environmental shear, even though they occur in small numbers. This could indicate other indirect effects of VWS that have opposite effects on cloud development if found to be significant in the future.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2018

Three-Dimensional Flow Behavior Inside the Submerged Entry Nozzle

According to various authors, the surface quality of steel depends on the dynamic conditions that occur within the continuous casting mold’s upper region. The meniscus, found in that upper region, is where the solidification process begins. The liquid steel is distributed into the mold through a submerged entry nozzle (SEN). In this paper, the dynamic behavior inside the SEN is analyzed by means of physical experiments and numerical simulations. The particle imaging velocimetry technique was used to obtain the vector field in different planes and three-dimensional flow patterns inside the SEN volume. Moreover, large eddy simulation was performed, and the turbulence model results were used to understand the nonlinear flow pattern inside the SEN. Using scaled physical and numerical models, quasi-periodic behavior was observed due to the interaction of two three-dimensional vortices that move inside the SEN lower region located between the exit ports of the nozzle.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Evidence of Mixed Scaling for Mean Profile Similarity in the Stable Atmospheric Surface Layer

A new mixed scaling parameter Z = z/(Lh)1/2 is proposed for similarity in the stable atmospheric surface layer, where z is the height, L is the Obukhov length, and h is the boundary layer depth. In comparison with the parameter ζ = z/L from Monin–Obukhov similarity theory (MOST), the new parameter Z leads to improved mean profile similarity for wind speed and air temperature in large-eddy simulations. It also yields the same linear similarity relation for CASES-99 field measurements, including in the strongly stable (but still turbulent) regime where large deviations from MOST are observed. Results further suggest that similarity for turbulent energy dissipation rate depends on both Z and ζ. The proposed mixed scaling of Z and relevance of h can be explained by physical arguments related to the limit of z-less stratification that is reached asymptotically above the surface layer. The presented evidence and fitted similarity relations are promising, but the results and arguments are limited to a small sample of idealized stationary stable boundary layers. Here, corroboration is needed from independent datasets and analyses, including for complex and transient conditions not tested here.

54 ENVIRONMENTAL SCIENCES↗