Constant Flux Layer Research Articles

Impact of Dust Source Patchiness on the Existence of a Constant Dust Flux Layer During Aeolian Erosion Events

AbstractDust emission fluxes during wind soil erosion are usually estimated using a dust concentration vertical gradient, by assuming a constant dust flux layer between the surface and the dust measurement levels. Here, we investigate the existence of this layer during erosion events recorded in Iceland and Jordan. Size‐resolved dust fluxes were estimated at three levels between 2 and 4 m using the eddy‐covariance method. Dust fluxes were found mainly constant only between the two upper levels in Iceland, the lower dust flux being often stronger and richer in coarse particles, while dust fluxes in Jordan were nearly constant across all levels. The wind dynamics could not explain the absence of a constant dust flux layer in Iceland. We show that the presence of stationary dust source patches in Iceland, related to surface humidity, created a non‐uniform dust layer near the surface, named dust roughness sublayer (DRSL), where individual plumes behind each patch interact but do not fully mix. The lowest dust measurement level was probably located within this sublayer while the upper ones were located above, such that there the emitted dust became spatially well‐mixed. This explains near the surface in Iceland, the more intermittent dust concentration, its low correlation with the dust concentrations above, and the richer dust flux in coarse particles due to their lower deposition contribution. Our findings highlight the importance of estimating dust fluxes above a dust blending height whose characteristics depend on the dust source patchiness caused by surface humidity or the presence of sparse non‐erosive elements.

An empirical study of the influences of gustiness on vertical mixing at the air-sea boundary

The exchange of momentum across the air-sea interface is a key driver of the earth system and its accurate parameterization is essential for precise weather and climate forecasting. However, our understanding of gustiness as an independent factor that can contribute to the momentum flux is limited. Using data collected from the R/P FLIP, as part of the Couple Air-Sea Processes and Electromagnetic ducting Research (CASPER) experiment, we explored the mechanisms by which gustiness contributes to the total interfacial momentum flux. We investigate how gustiness affects both the temporal and spatial (vertical) variance of turbulence in the atmospheric surface layer and show that high gustiness was associated with strong anisotropic turbulence at each measurement height. This was found to increase vertical wind fluctuations and inject additional momentum across the air-sea interface at lower wind speeds. Increased gustiness was also associated with the breakdown of the constant flux layer, which is generally assumed to exist over the ocean. This study has implications for both momentum flux parameterization and the use of similarity theory to model the flux-gradient relationship in the gusty atmospheric surface layer, thereby influencing the forecasting of climate and weather.

Current shear and turbulence during a near-inertial wave

Surface currents and turbulent mixing were observed during a near-inertial wave (NIW) using an accousting doppler current profiler (ADCP) and satellite-tracked drifters. Drifter trajectories sampled at three depth levels show characteristics of an Ekman solution superposed with the NIW. Velocity and dissipation estimates from the ADCP reveal strong shear with a distinct constant flux layer in between the roughness length and a critical depth at 4m. Below, a shear free slab layer performing an inertial oscillation is observed. Dissipation, as estimated from the vertical beam of the ADCP, peaks in the wave-enhanced friction layer when the current opposes the wind and wave direction. Below the constant flux layer, maximum turbulence is observed when the NIW is in a phase that is in opposite direction to the time-averaged current. During this phase, currents at various depths rapidly realign in the entire boundary layer.

Eddy covariance assessment of alternate wetting and drying floodwater management on rice methane emissions

Reducing methane emissions and water use is critical for combating climate change and declining aquifers on food production. Reductions in irrigation water use and methane emissions are known benefits of practicing alternate wetting and drying (AWD) over continuous flooding (CF) water management in lowland rice (Oryza sativa L.) production systems. In a two-year (2020 and 2021) study, methane emissions from large farm-scale (∼50 ha) rice fields managed under CF and AWD in soils dominated by Sharkey clay (Sharkey clay, clay over loamy, montmorillonitic non-acid, thermic Vertic halauepet) were monitored using the eddy covariance method (EC). In the EC system, an open-path laser gas analyzer was used to monitor air methane gas density in the constant flux layer of the atmosphere over the rice-crop canopies. Total water pumped into the field for floodwater management was higher in CF compared to AWD by 24 and 14% in 2020 and 2021, respectively. Considerable variations between seasons in the amount of methane emitted from the CF and AWD treatments were observed: CF emitted 29 and 75 kg ha−1 and AWD emitted 14 and 34 kg ha−1 methane in 2020 and 2021, respectively. Notwithstanding, the extent of reduction in methane emissions due to AWD over CF was similar for each crop season (52% in 2020 and 55% in 2021). Rice grain yield harvested differed by only ±2% between AWD and CF. This investigation of large-scale system-level evaluation, using the EC method, confirmed that by practicing AWD floodwater management in rice, water pumped from aquifers could be reduced by about a quarter and methane emissions from rice fields could be cut down by about half without affecting grain yields, thereby promoting sustainable water management and greenhouse gas emission reduction during rice production in the Lower Mississippi Delta.

Improving Wave‐Based Air‐Sea Momentum Flux Parameterization in Mixed Seas

AbstractIn winter, the Northwest Tropical Atlantic Ocean can be characterized by various wave age‐based interactions among ocean current, surface wind and surface waves, which are critical for accurately describing surface wind stress. In this work, coupled wave‐ocean‐atmosphere model simulations are conducted using two different wave roughness parameterizations within COARE3.5, including one that relies solely on wind speed and another that uses wave age and wave slope as inputs. Comparisons with the directly measured momentum fluxes during the ATOMIC/EUREC4A experiments in winter 2020 show that, for sea states dominated by short wind waves under moderate to strong winds, the wave‐based formulation (WBF) increases the surface roughness length in average by 25% compared to the wind‐speed‐based approach. For sea states dominated by remotely generated swells under moderate to strong wind intensity, the WBF predicts significantly lower roughness length and surface stress (≈15%), resulting in increased near‐surface wind speed above the constant flux layer (≈5%). Further investigation of the mixed sea states in the model and data indicates that the impact of swell on wind stress is over‐emphasized in the COARE3.5 WBF, especially under moderate wind regimes. Various approaches are explored to alleviate this deficiency by either introducing directional alignment between wind and waves or using the mean wave period instead of the wave period corresponding to the spectral peak to compute the wave age. The findings of this study are likely to be site‐dependent, and mostly concern specific regimes of wind and waves where the original parameterization was deficient.

Observations of boundary layer wind and turbulence of a landfalling tropical cyclone

This study investigates the atmospheric boundary layer structure based on multiple-level tower observations with a height of 350 m during the landfall of Super Typhoon Mangkhut (2018). Results show a layer of log wind profile outside of the radius of maximum wind speed with a height of 100 m or larger. The log layer height increases with the wind speed. The height of the constant flux layer reaches ~ 300 m for 10-m wind speeds less than 13 m s−1 while this height decreases with the wind speed. Momentum fluxes and turbulent kinetic energy increase with the wind speed at all vertical levels. The drag coefficient and surface roughness length estimated at the tower location have values of 7.3 × 10–3 and 0.09 m, respectively, which are independent of wind speed. The estimated vertical eddy diffusivity and mixing length increase with height up to ~ 160 m and then slowly decrease with height. The vertical eddy diffusivity increases with the wind speed while the vertical mixing length has no dependence on the wind speed. Comparing our results with previous work indicates that the vertical eddy diffusivity is larger over land than over ocean at a given wind speed range.

Characteristics and Scaling of the Stable Marine Internal Boundary Layer

AbstractThe characteristics of a stable internal boundary layer (SIBL) offshore of Duck, North Carolina documented during CASPER‐EAST have been examined using surface layer‐resolving large eddy simulations. Under the influence of steady offshore winds, a SIBL develops over the coastal waters with its depth growing with the offshore advection time (TA) as ∼. The SIBL includes an internal equilibrium layer above the surface where the heat and momentum fluxes linearly decrease with height and a transition layer aloft. The offshore area can be partitioned into three distinct zones, namely, a nearshore zone (NSZ, TA < Td/3), an intermediate offshore zone (IOZ, Td/3 < TA < Td), and a far‐offshore zone (FOZ, TA > Td), where Td is the vertically‐averaged turbulent dissipation time. The advection of turbulence from land plays a significant role in the momentum and scalar budgets over the NSZ. Consequently, the Monin‐Obukhov similarity theory (MOST) becomes invalid, and local similarity theory is applicable only above the SIBL in the NSZ. In the IOZ, the advection of turbulence from land is less important but still non‐negligible. As a result, while the dimensionless standard deviations of winds and potential temperature converge toward the MOST curves, the dimensionless gradients are smaller than their counterparts in the FOZ. In the FOZ, the advection from land becomes negligible, and MOST is applicable throughout the constant flux layer. Over the IOZ and the FOZ, LST works reasonably well within the SIBL.

High Grashof number turbulent natural convection on an infinite vertical wall

The present study concerns a temporally evolving turbulent natural convection boundary layer (NCBL) adjacent to an isothermally heated vertical wall, with Prandtl number 0.71. Three-dimensional direct numerical simulations (DNS) are carried out to investigate the turbulent flow up to $\textit {Gr}_\delta =1.21\times 10^8$ , where $\textit {Gr}_\delta$ is the Grashof number based on the boundary layer thickness $\delta$ . In the near-wall region, there exists a constant heat flux layer, similar to previous studies for the spatially developing flows (e.g. George & Capp, Intl J. Heat Mass Transfer, vol. 22, 1979, pp. 813–826). Beyond a wall-normal distance $\delta _i$ , the NCBL can be characterised as a plume-like region. We find that this region is well described by a self-similar integral model with profile coefficients (cf. van Reeuwijk & Craske, J. Fluid Mech., vol. 782, 2015, pp. 333–355) which are $\textit {Gr}_\delta$ -independent after $\textit {Gr}_\delta =10^7$ . In this Grashof number range both the outer plume-like region and the near-wall boundary layer are turbulent, indicating the beginning of the so-called ultimate turbulent regime (Grossmann & Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56; Grossmann & Lohse, Phys. Fluids, vol. 23, 2011, 045108). Solutions to the self-similar integral model are analytically obtained by solving ordinary differential equations with profile coefficients empirically obtained from the DNS results. In the present study, we have found the wall heat transfer of the NCBL is directly related to the top-hat scales which characterise the plume-like region. The Nusselt number is found to follow $\textit {Nu}_\delta \propto \textit {Gr}_\delta ^{0.381}$ , slightly higher than the empirical $1/3$ -power-law correlation reported for spatially developing NCBLs at lower $\textit {Gr}_\delta$ , but is shown to be consistent with the ultimate heat transfer regime with a logarithmic correction suggested by Grossmann & Lohse (Phys. Fluids, vol. 23, 2011, 045108). By modelling the near-wall buoyancy force, we show that the wall shear stress would scale with the bulk velocity only at asymptotically large Grashof numbers.

Evaluation of Profiles of Standard Deviation of Vertical Wind in the Urban Area of Rome: Performances of Monin–Obukhov Similarity Theory Using Different Scaling Variables

The parametrizations of meteorological variables provided by the Monin–Obukhov similarity theory (MOST) is of major importance for pollutant dispersion assessment. However, the complex flow pattern that characterizes the urban areas limits the applicability of the MOST. In this work, the performance of different existing parametrizations of the standard deviation of vertical wind velocity were tested in the city of Rome. Results were compared with experimental data acquired by a sonic detection and ranging (SODAR) and a sonic anemometer. Different scaling variables estimated from the anemometer data by considering two coordinate systems—one aligned with the geodetic reference frame and the other following the flow streamlines—were used to evaluate the effects of flow distortion due to the presence of buildings. Results suggest that the MOST parametrizations perform better if the scaling variables obtained using the coordinate system following the flow streamlines are used. This estimation of the scaling variables would make it possible to overcome the difficulties in conducting measurements of turbulent fluxes, either at different altitudes or even in the constant flux layer.

Comparison Between Eddy‐Covariance and Flux‐Gradient Size‐Resolved Dust Fluxes During Wind Erosion Events

AbstractEstimating accurately dust emission flux during aeolian erosion events is crucial for quantifying the amount of dust in the atmosphere. The rare existing field experiments quantifying such flux were mainly performed using the flux‐gradient (FG) method. Here, we present the first intercomparison of the size‐resolved dust fluxes estimated by both the FG and the eddy‐covariance (EC) methods during several erosion events. Both methods were applied simultaneously during the WIND‐O‐V (WIND erOsion in presence of sparse Vegetation)'s 2017 field experiment over an isolated erodible bare plot in South Tunisia. Overall, both methods predict similar dust fluxes for particle smaller than about 4 μm. For coarser particles, the EC method predicts a smaller dust flux than the FG method. Factors explaining this difference are discussed such as the different sampling heads used by the dust particle counters of both methods, or the possible weakening of the constant dust flux layer at the location of the upper dust particle counter of the FG method. This intercomparison highlights the difficulties and advantages of each method as well as their complementarity.

Mean thermal energy balance analysis in differentially heated vertical channel flows

Direct numerical simulations of differentially heated vertical channel (DHVC) flows were performed for Ra=105–109 to investigate the characteristics of the streamwise mean momentum and mean thermal energy equations. The log law for mean temperature was observed for Ra≥108 at y+>50, where y+ is the wall-normal distance normalized by the viscous wall unit. From the mean momentum equation, negligible viscous force and logarithmically increasing Reynolds shear stress were observed in the region where the log law for mean temperature occurred. The streamwise mean velocity did not exhibit a linear relationship with y+ close to the wall and did not show logarithmic development far from the wall due to the buoyancy force. In the mean thermal energy equation, a constant heat flux layer was observed, and the turbulent heat flux contribution was scaled by the inverse of wall-normal distance to satisfy the log law of mean temperature. For a high Rayleigh number (Ra=109), the turbulent heat flux spectra contained scale-separated inner and outer sites with linearly growing energetic structures along the wall-normal distance, which was not observed for a low Rayleigh number (Ra=106). The flow structures of turbulent heat flux originated from the upward wall-normal velocity fluctuations that triggered the non-directional structures of the temperature. These results suggest that the scale separation between the viscous and outer length scales with the wall-attached energetic structures resulted in the log law for mean temperature. These findings could serve as the basis of scaling formulations for the mean velocity and temperature in DHVC flows.

An Evaluation of the Constant Flux Layer in the Atmospheric Flow Above the Wavy Air‐Sea Interface

AbstractThe constant flux layer assumption simplifies the problem of atmospheric surface layer (ASL) dynamics and is an underlying assumption of Monin‐Obukhov similarity theory (MOST), which is ubiquitously applied to model interfacial exchange and atmospheric turbulence. Within the marine environment, the measurements necessary to confirm the local ASL as a constant flux layer are rarely available, namely: direct observations of the near‐surface flux gradients. Recently, the Research PlatformFLIPwas deployed with a meteorological mast that resolved the momentum and heat flux gradients from 3 to 16 m above the ocean surface. Here, we present an assessment of the prevalence of the constant flux layer within the ASL, using an approach that accounted for the role of wave‐coherent motion in air and evaluated each observed flux gradien. Our analysis revealed that only 30%–40% of momentum flux gradients were approximately constant; for the heat fluxes, this increased to 50%–60%. For low winds, the stationarity of local turbulence was critical to the constant flux layer's validity, but resulted in excising a large proportion of the observed profiles. Under moderate wind speeds, swell‐wind alignment was associated with momentum flux divergence. Our findings suggest that the constant flux layer, as it is conventionally defined, is not generally valid over the ocean. This holds significant implications for measuring air‐sea fluxes from single point sources and marine applications of MOST.

Swell Modulation on Wind Stress in the Constant Flux Layer

AbstractThe impact of swell on wind stress is investigated through direct three‐layer flux measurements taken by a fixed tower in the marine atmospheric boundary layer. Observations confirm that the assumption of constant momentum flux layer is valid under swell‐dominated conditions around the reference height of 10 m. The swell can modulate the total wind stress to be less than the turbulent stress derived from the first‐order closure method, and the extent of this modulation decreases with height. The critical layer that represents the top of the layer affected by stronger swells is estimated to reach 45‐m altitude, and the depth of this layer decreases as the swells weaken and the wind speed increases. Furthermore, a simple swell correction scheme for the total stress calculation is developed, showing good performance against observations.

Law of the wall for a temporally evolving vertical natural convection boundary layer

Abstract

Quantifying evapotranspiration and crop coefficients for cotton (Gossypium hirsutum L.) using an eddy covariance approach

Accurate quantification of consumptive water requirements (ETc, evapotranspiration) of cropping systems is a critical prerequisite for sustainable irrigation water management applications. For applying the ETc for irrigation scheduling across soils and climates other than the location in which it was measured, it is also critical to develop crop coefficients (Kc) that link a reference crop evapotranspiration computed from local weather data to ETc. A systematic study for deriving Kc for cotton (Gossypium hirsutum L.) - representing its growth stages from planting to harvest - in humid climates is lacking in the literature. In this study, we used an eddy covariance (EC) method to quantify ETc from irrigated cotton (Gossypium hirsutum L.) in a 250 ha field with a Tunica clay soil, in 2017 and 2018. In the EC experiment, an open-path infrared gas analyzer and a sonic 3-D anemometer were deployed in the constant flux layer above the cotton canopy for collecting crop-canopy water flux data. Using the measured ETc, Kc were derived for alfalfa (Kcr) and grass (Kco) reference crop ET computed from weather data. Cotton cv. Delta Pine Land 1522 was planted in the first week of May and harvested in the second week of September in both the years. Lint yield was 1269 kg ha−1 in 2017 and 1569 kg ha−1 in 2018. Measured monthly averaged daily ETc ranged between 2.5 mm in May/September to 4 mm in July in 2017, and between 2.9 mm in May and 4.4 mm in August in 2018. Maximum daily ETc in 2017 and 2018 crop seasons were 5.6 and 6.7 mm, respectively. Seasonal total ETc was 367 mm and 439 mm (on average 402 mm), respectively. Alfalfa (ETr) and grass reference crop ET (ETo) computed were 664 and 546 mm, respectively. Averaged across the two years, average daily Kcr ranged between 0.45 in May to 0.80 in August, and Kco ranged from 0.54 in May and 0.99 in August. On average, seasonal ETr was 18 % more than ETo. Seasonal ETr and ETo were, respectively, 39 % and 22 % more than ETc. The Kc data developed will be useful for irrigation scheduling in cotton grown in similar climates and soils.

Scaling of Dust Flux With Friction Velocity: Time Resolution Effects

AbstractThe intermittency of aeolian soil erosion has motivated studies to extend to small time resolution (less than 15–30 min) the scaling property of erosion fluxes with the friction velocity . However, common methods used to estimate such as the law of the wall or the eddy covariance are only valid for stationary conditions, that is, long periods of 15–30 min. Unlike these methods, the wavelet transform method is applicable for nonstationary conditions. Here, this method is used to investigate the scaling property of the dust flux with at 1‐min and 10‐s resolutions, during erosion events. At 15‐min resolution, and estimated from the wavelet transform are identical to those obtained by eddy covariance. At smaller resolution, and exhibit strong fluctuations around their 15‐min trend, reflecting the nonstationarity of the flow and the intermittency of dust emission, respectively. While the 15‐min resolution appears as correlated with as with the mean wind speed , with decreasing resolution, becomes less correlated with but still significantly correlated with . Our results suggest that is a suitable scaling parameter of over usual 15‐ to 30‐min periods with the advantage of being height independent compared to . However, at small time resolution, becomes more relevant to scale , the surface friction velocity becoming hardly accessible due to the absence of a constant momentum flux layer. Our study demonstrates the suitability of the wavelet transform to estimate dust fluxes at small time resolution or during nonstationary events.

The study of a turbulent air flow over capillary-gravity water surface waves by direct numerical simulation

The present study is concerned with direct numerical simulation (DNS) of turbulent air flow over a waved water surface. Three-dimensional, turbulent Couette flow is considered in DNS as a model of a constant-flux layer in the marine atmospheric surface layer. Two-dimensional stationary waves at the water surface are prescribed and assumed to be unaffected by the air-flow. We consider capillary-gravity water surface waves and are interested in the influence of “parasitic” capillary ripples riding on the carrier, energy-containing waves, on the properties of the air-flow. The surface waves are prescribed and considered to be stationary, the capillaries being in phase with the carrier wave. The surface elevations spectra are also prescribed and mimicking stationary capillaries riding on Stokes waves observed in a 2D numerical simulation of water-surface capillary-gravity waves by Hung & Tsai (2009). The bulk air velocity and the carrier water surface waves lengths are considered in our DNS in the range of 3 to 5 m/s and 3 to 7 cm, respectively. Under these conditions, the capillaries are found to be submerged within the viscous sublayer of the atmospheric boundary layer. Our DNS results show that although the flow fields are characterized by instantaneous separations of the boundary layer, the ensemble (wave-phase) averaged flow fields are non-separating and well predicted by a quasilinear theoretical model. We find also that capillaries mitigate the development of coherent (horse-shoe) vortex structures as compared to the no-ripples flow-case. We further use DNS results and quasilinear model formulation to parameterize the water surface roughness height in terms of critical layer thickness and the amplitude of a dominant, energy-containing harmonic of the water surface elevation spectrum.

Large-Eddy Simulation Study of Log Laws in a Neutral Ekman Boundary Layer

Abstract The characteristics of wind profiles in a neutral atmospheric boundary layer and their dependence on the geostrophic wind speed Ug, Coriolis parameter f, and surface roughness length z0 are examined utilizing large-eddy simulations. These simulations produce a constant momentum flux layer and a log-law layer above the surface characterized by a logarithmic increase of wind speed with height. The von Kármán constant derived from the mean wind profile is around 0.4 over a wide range of control parameters. The depths of the simulated boundary layer, constant-flux layer, and surface log-law layer tend to increase with the wind speed and decrease with an increasing Coriolis parameter. Immediately above the surface log-law layer, a second log-law layer has been identified from these simulations. The depth of this upper log-law layer is comparable to its counterpart in the surface layer, and the wind speed can be scaled as , as opposed to just in the surface log-law layer, implying that in addition to surface processes, the upper log-law layer is also influenced by Earth’s rotation and large-scale conditions. Here is the friction velocity at the surface, and h is the boundary layer depth. An analytical model is proposed to assist in the interpretation of the log laws in a typical Ekman boundary layer. The physics and implications of the upper log-law layer are discussed.

Winds near the Surface of Waves: Observations and Modeling

AbstractThe concept of a constant-flux layer is usually employed for vertical profiling of the wind measured at some elevation near the ocean surface. The surface waves, however, modify the balance of turbulent stresses very near the surface, and therefore such extrapolations can introduce significant biases. This is particularly true for buoy measurements in extreme conditions, when the anemometer mast is within the wave boundary layer (WBL) or even below the wave crests. In this paper, field data and a WBL model are used to investigate such biases. It is shown that near the surface the turbulent stresses are less than those obtained by extrapolation using the logarithmic-layer assumption, and the mean wind speeds very near the surface, based on Lake George field observations, are up to 5% larger. The behavior is then simulated by means of a WBL model coupled with nonlinear waves, which confirmed the observations and revealed further details of complex behaviors at the wind-wave boundary layer.

Intrinsic Constraints on Asymmetric Turbulent Transport of Scalars Within the Constant Flux Layer of the Lower Atmosphere

AbstractA widely used assumption in boundary layer meteorology is the z independence of turbulent scalar fluxes Fs throughout the atmospheric surface layer, where z is the distance from the boundary. This assumption is necessary for the usage of Monin‐Obukhov Similarity Theory and for the interpretation of eddy covariance measurements of Fs when using them to represent emissions or uptake from the surface. It is demonstrated here that the constant flux assumption offers intrinsic constraints on the third‐order turbulent transport of Fs in the unstable atmospheric surface layer. When enforcing z independence of Fs on multilevel Fs measurements collected above different surface cover types, it is shown that increasing instability leads to a novel and universal description of (i) the imbalance between ejecting and sweeping eddy contributions to Fs and (ii) the ratio formed by a dimensionless turbulent transport of Fs and a dimensionless turbulent transport of scalar variance. When combined with structural models for the turbulent transport of Fs, these two findings offer a new perspective on “closing” triple moments beyond conventional gradient diffusion schemes. A practical outcome is a diagnostic of the constant flux assumption from single‐level Fs measurements.