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Abstract: Abstract This study investigates the parameterization of the geostrophic drag law (GDL) for conventionally neutral atmospheric boundary layers (CNBLs). Utilizing large eddy simulations, we confirm that in CNBLs capped by a potential temperature inversion, the boundary-layer height scales as \(u_*/\sqrt{N f}\) , where \(u_*\) represents the friction velocity, N the free-atmosphere Brunt–Väisälä frequency, and f the Coriolis parameter. Additionally, we confirm that the wind gradients normalized by the Brunt–Väisälä frequency have universal profiles above the surface layer. Leveraging these physical insights, we derived analytical expressions for the GDL coefficients A and B, correcting the earlier form of Zilitinkevich and Esau (Q J R Meteorol Soc 131:1863–1892, 2005). These expressions for A and B have been validated numerically, ensuring their accuracy in representing the geostrophic drag coefficient \(u_*/G\) (G is the geostrophic wind speed) and the cross-isobaric angle. This work extends the range for which the GDL has been validated up to \(u_*/G =[0.019, 0.047]\) . This further supports the application of GDL to CNBLs over a broader range of \(u_*/G\) , which is useful for meteorological applications such as wind energy. PubDate: 2024-08-10

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Abstract: Abstract Zero plane displacement height ( \(d_0\) ) and momentum roughness length ( \(z_{0m}\) ), describe the aerodynamic characteristics of a vegetated surface. Usually, \(d_0\) and \(z_{0m}\) are assumed to be constant functions of the physical characteristics of the surface. Prior evidence collected from the literature and our examination of flux tower data show that \(d_0\) and \(z_{0m}\) vary in time at sites with tree and shrub canopies, but not grasslands. The conventional explanations of these variations are based on linear functions of wind velocity and friction velocity, with little theoretical basis. This study explains the variation in aerodynamic parameters by matching four analytical canopy velocity models to a logarithmic above-canopy velocity profile at canopy height. \(d_0\) and \(z_{0m}\) come out as functions of 2 non-dimensional terms, the canopy momentum absorption capacity (parameter) and a (measurable) Péclet number. To test the theories of variation, we analysed the velocity profiles from Ozflux and Ameriflux sites. None of the theories could recreate \(d_0\) and \(z_{0m}\) at half-hourly intervals. However, the canopy velocity models were able better to recreate the distribution of the variations in \(d_0\) and \(z_{0m}\) . Additionally, the estimates of canopy momentum absorption capacity varied consistently with phenological changes in the canopies, whereas, the fitting parameters of the linear regression of using wind speed and friction velocity did not exhibit physically interpretable variations. The canopy velocity models may offer better predictions with an accurate estimation of the canopy height, a horizontally homogeneous and rigid canopy, and incorporation of the roughness sublayer. PubDate: 2024-08-01

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Abstract: Abstract An experiment was carried out using a scale model of a tall building, with the goal of investigating the role of individual buildings in the dispersion of air pollution. Pollutant dispersion around an isolated building with a height-to-length aspect ratio of 1.4 is investigated using simultaneous particle image velocimetry and planar laser induced fluorescence. Dye is released from a ground-level point source five building heights upstream of the tall building. It was found that in this case the scalar plume was dispersed laterally strongly by the building, but only slightly vertically. It is hypothesized that this is due to 94% of the plume impinging below the stagnation point on the front of the building and being drawn into the horseshoe vortex. We expect this fraction would be lower in a case in which the building is in an array of smaller buildings, and that this would lead to more vertical dispersion. PubDate: 2024-07-16

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Abstract: Abstract We propose the multivariate locally stationary wavelet (mvLSW) process to analyze surface turbulent fluxes in nonstationary atmospheric conditions. Using theoretical spectral characteristics, we generated synthetic data representing stationary and nonstationary turbulence time series. This data enables us to explore the impact of mesoscale atmospheric flows on the stationary microscale turbulence field and detect the spectral gap in the time-varying cospectra. Applying this approach to experimental data collected in Fairbanks, Alaska and Bogota, Colombia, we demonstrated the ability to detect cospectral gaps and compute bandwidth-limited turbulent fluxes arising from stationary components of the atmospheric flow. These findings underscore the importance of considering scale-dependent atmospheric forcing when comparing model and experimental data. PubDate: 2024-07-15

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Abstract: Abstract Near-surface similarities and atmospheric turbulence characteristics have a large impact on numerical weather prediction models. However, the validity of these similarities is unclear during precipitation. This study investigates the modulations in atmospheric boundary layer turbulence and the variations of the near-surface scaling similarities caused by rainfall. Here we present our field observations on the effects of rainfall on the near-surface similarities and atmospheric turbulence in the stable boundary layer using a Parsivel2 disdrometer and a 3D ultrasonic anemometer at our outdoor rainfall laboratory in San Antonio, Texas, USA. During moderate to heavy rainfall conditions, higher turbulent energy was observed than those in non-rainy conditions when the turbulence intensity and the wind speeds were relatively low. On the contrary, when the turbulence intensity and the wind speeds were relatively high, the turbulence energy in the stable boundary layer were dampened due to the raindrops. Raindrops with high particle Reynolds numbers ( \(Re_{p} = D_{m} v_{t} /\vartheta\) ; \(D_{m}\) —mean volume diameter, \({v}_{t}\) —terminal raindrop fall speed, and \(\vartheta\) —kinematic viscosity of the surrounding air) can act as either a source or a sink of turbulent kinetic energy depending on the turbulence intensity of the atmosphere. Our field observations showed that near-surface similarities deviated from the scaled similarities under the influence of rainfall. The normalized standard deviations of the streamwise and vertical velocity components and the dissipation rate were higher during rainy than non-rainy times. Rainfall effects on turbulence modulations and near-surface scaling parameters of the stable boundary layer are discussed with considerations of the relevant mechanisms. PubDate: 2024-07-13

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Abstract: Abstract In this study, we present an extension to the Monin–Obukov similarity theory (MOST) for the roughness sublayer (RSL) over short vegetation. We test our theory using temperature measurements from fiber optic cables in an array-shaped set-up. This provides a high vertical measurement resolution that enables us to measure the sharp temperature gradients near the surface. It is well-known that MOST is invalid in the RSL as the flow is distorted by roughness elements. However, to derive the surface temperature, it is common practice to extrapolate the logarithmic profiles down to the surface through the RSL. Instead of logarithmic behaviour defined by MOST near the surface, our observations show near-linear temperature profiles. This log-to-linear transition is described over an aerodynamically smooth surface by the Van Driest equation in classical turbulence literature. Here we propose that the Van Driest equation can also be used to describe this transition over a rough surface, by replacing the viscous length scale with a surface length scale \(L_s\) that represents the size of the smallest eddies near the grass structures. We show that \(L_s\) scales with the geometry of the vegetation and that the model shows the potential to be scaled up to tall canopies. The adapted Van Driest model outperforms the roughness length concept in describing the temperature profiles near the surface and predicting the surface temperature. PubDate: 2024-06-21

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Abstract: Abstract Simulations of the processes contributing to the deposition of trace gases and small particles from the air to natural surfaces routinely describe the consequences of changing molecular diffusivity in terms of the Schmidt number, Sc ≡ ν/D, where ν is kinematic viscosity and D the molecular diffusivity of the constituent in question. Using well-verified results of pipe flow experiments, early workers proposed that the relevant property entering dry deposition and other models of similar kind should be Sc−2/3 rather than Sc−1 as would be expected from historic flat plate experiments. Upon reconsideration, it is now proposed that no universal power-law dependence on Sc can be expected; the corresponding role of molecular diffusivity is likely to be site-specific. Relevant experimental evidence remains elusive. PubDate: 2024-06-12 DOI: 10.1007/s10546-024-00857-x

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Abstract: Abstract In this study, a systematic mathematical analysis has been presented for the extent of applicability of various non-linear similarity functions for momentum \(({{\upvarphi }}_{{\text{m}}})\) and heat \(({{\upvarphi }}_{{\text{h}}})\) under stable conditions to compute surface turbulent fluxes in numerical models. The investigation is carried out for equal and unequal momentum \(({{\text{z}}}_{0})\) and heat \(({{\text{z}}}_{{\text{h}}})\) roughness lengths. The study reveals that \({{\upvarphi }}_{{\text{m}}}\) and \({{\upvarphi }}_{{\text{h}}}\) utilized in the National Centre for Atmospheric Research Community Atmosphere Model version 5 (NCAR-CAM5) (Holtslag et al. in Mon Weather Rev 118:1561–1575, 1990) have several restrictions on their applicability in moderately to strongly stable cases. If the ratios of \({{\text{z}}}_{0}\) and \({{\text{z}}}_{{\text{h}}}\) to the height \(({\text{z}})\) from the surface (i.e., \(\frac{{{\text{z}}}_{0}}{{\text{z}}}\) and \(\frac{{{\text{z}}}_{{\text{h}}}}{{\text{z}}}\) ) lie in the range \((0.2, 1)\) , the functions are valid for a limited range of \(\upzeta \) (stability parameter) in strong stable conditions \(\left(\upzeta >1\right)\) ; however, when \(\frac{{{\text{z}}}_{0}}{{\text{z}}}\le 0.2\) and \(\frac{{{\text{z}}}_{{\text{h}}}}{{\text{z}}}\le 0.2\) , the validity of functions is unrestricted. In terms of bulk Richardson number \(\left({{\text{Ri}}}_{{\text{B}}}\right)\) , the functions are valid for a limited range of moderately to strongly stable conditions. These theoretically derived upper limits have also been validated using observations from the UK Meteorological Office’s Cardington and Cooperative Atmosphere-Surface Exchange Study-99 datasets. On the other hand, similarity functions based on Cheng and Brutsaert (Boundary-Layer Meteorol 114:519–538, 2005), Grachev et al. (Boundary-Layer Meteorol 124:315–333, 2007), Srivastava et al. (Meteorol Appl 27, 2020), and Gryanik et al. (J Atmos Sci 77:2687–2716, 2020) are found to be theoretically valid for all values of \(\upzeta \) and \({{\text{Ri}}}_{{\text{B}}}\) . The efforts have also been made to implement these functions in the Weather Research and Forecasting as well as global scale models. PubDate: 2024-06-01 DOI: 10.1007/s10546-024-00869-7

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Abstract: Abstract Large-eddy simulations are used to evaluate mean profile similarity in the convective boundary layer (CBL). Particular care is taken regarding the grid sensitivity of the profiles and the mitigation of inertial oscillations in the simulation spin-up. The nondimensional gradients \(\phi \) for wind speed and air temperature generally align with Monin–Obukhov similarity across cases but have a steeper slope than predicted within each profile. The same trend has been noted in several other recent studies. The Businger-Dyer relations are modified here with an exponential cutoff term to account for the decay in \(\phi \) to first-order approximation, yielding improved similarity from approximately 0.05 \(z_i\) to above 0.3 \(z_i\) , where \(z_i\) is the CBL depth. The necessity for the exponential correction is attributed to an extended transition from surface scaling to zero gradient in the mixed layer, where the departure from Monin–Obukhov similarity may be negligible at the surface but becomes substantial well below the conventional surface layer height of 0.1 \(z_i\) . PubDate: 2024-05-25 DOI: 10.1007/s10546-024-00870-0

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Abstract: Abstract The backdrop for this study is a knowledge gap about how turbulence anisotropy relates to the dissimilar transport of momentum and scalars. We use single-level measurements of turbulence over an alpine glacier for exploring the dissimilar transport of momentum, heat, and moisture in stably stratified katabatic flows. Our study is motivated by the need of addressing their flux dissimilarity from a fresh perspective of anisotropic motions of turbulence. Its objective is to promote new understanding of boundary-layer turbulence anisotropy as one possible factor in dissimilar behaviours between momentum and scalar transport over a sloping terrain. Specifically, the momentum–heat flux correlation ( \({R}_{{F}_{uT}}\) ) and the heat–moisture flux correlation ( \({R}_{{F}_{Tq}}\) ) coefficients vary across three different bulk states of kinetic anisotropy. Those states, identified using the barycentric Lumley map, suggest the predominance of two-component turbulence (being axisymmetric or not) and miscellaneous turbulence (whose topological shape is less salient). Miscellaneous turbulence typically bears a higher degree of the flux similarity between momentum and heat (i.e., \({R}_{{F}_{uT}}\) > 0.6) but a lower degree of that between heat and moisture (i.e., \(\left {R}_{{F}_{Tq}}\right \) < 0.7). The multi-resolution decomposition technique is then applied to identify larger-scale eddies of two-component topology, intermediate-scale eddies of oblate topology, and smaller-scale eddies of isotropic topology. Further analysis shows that an explicit change in eddy scale-wise topology is correlated not only with variations in \({R}_{{F}_{uT}}\) and \(\left {R}_{{F}_{Tq}}\right \) but with the dissimilar transport of momentum and scalars, so explaining a deviation from the Reynolds and the Lewis analogies in fluid mechanics. PubDate: 2024-05-13 DOI: 10.1007/s10546-024-00866-w

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Abstract: Abstract Studies on the shortwave spectrum, namely short-gravity, gravity-capillary, and parasitic-capillary waves, reveal that spectrum representation may modify the estimate of momentum transport at the air-sea interface. However, in numerical simulations, the shortwave spectra are usually approximated by simplified formulations. The effect of three shortwave spectrum formulations on the momentum balance at the air-sea interface was quantitatively evaluated for light to high wind speeds and fully developed seas. In the simulations, the spectra considered were: (i) obtained by an extrapolated function, (ii) dependent on the wave age derived from the observations, and (iii) from the solution of the energy balance equation. Considering computational time, the second was the fastest. while the first and third the computational time increased, respectively, by approximately 2–7% and 15–30%, depending on the wind speed. Concerning the observations, the mean square slope, the coupling parameter, and the drag coefficient, the second and third formulations showed better agreement, while the first one showed a large discrepancy. The results highlighted the importance of shortwave formulations in the analysis of the interaction between wind and wave. PubDate: 2024-05-11 DOI: 10.1007/s10546-023-00842-w

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Abstract: Abstract In absence of the high-frequency measurements of wind components, sonic temperature and water vapour required by the eddy covariance (EC) method, Monin–Obukhov similarity theory (MOST) is often used to calculate heat fluxes. However, MOST requires assumptions of stability corrections and roughness lengths. In most environments and weather situations, roughness length and stability corrections have high uncertainty. Here, we revisit the modified Bowen-ratio method, which we call C-method, to calculate the latent heat flux over snow. In the absence of high-frequency water vapour measurements, we use sonic anemometer data, which have become much more standard. This method uses the exchange coefficient for sensible heat flux to estimate latent-heat flux. Theory predicts the two exchange coefficients to be equal and the method avoids assuming roughness lengths and stability corrections. We apply this method to two datasets from high mountain (Alps) and polar (Antarctica) environments and compare it with MOST and the three-layer model (3LM). We show that roughness length has a great impact on heat fluxes calculated using MOST and that different calculation methods over snow lead to very different results. Instead, the 3LM leads to good results, in part due to the fact that it avoids roughness length assumptions to calculate heat fluxes. The C-method presented performs overall better or comparable to established MOST with different stability corrections and provides results comparable to the direct EC method. An application of this method is provided for a new station installed in the Pamir mountains. PubDate: 2024-05-04 DOI: 10.1007/s10546-024-00864-y

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Abstract: Abstract In the last decades the energy-balance-closure problem has been thoroughly investigated from different angles, resulting in approaches to reduce but not completely close the surface energy balance gap. Energy transport through secondary circulations has been identified as a major cause of the remaining energy imbalance, as it is not captured by eddy covariance measurements and can only be measured additionally with great effort. Several models have already been developed to close the energy balance gap that account for factors affecting the magnitude of the energy transport by secondary circulations. However, to our knowledge, there is currently no model that accounts for thermal surface heterogeneity and that can predict the transport of both sensible and latent energy. Using a machine-learning approach, we developed a new model of energy transport by secondary circulations based on a large data set of idealized large-eddy simulations covering a wide range of unstable atmospheric conditions and surface-heterogeneity scales. In this paper, we present the development of the model and show first results of the application on more realistic LES data and field measurements from the CHEESEHEAD19 project to get an impression of the performance of the model and how the application can be implemented on field measurements. A strength of the model is that it can be applied without additional measurements and, thus, can retroactively be applied to other eddy covariance measurements to model energy transport through secondary circulations. Our work provides a promising mechanistic energy balance closure approach to 30-min flux measurements. PubDate: 2024-05-04 DOI: 10.1007/s10546-024-00868-8

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Abstract: Abstract The present paper shows that local similarity theories, proposed for the strongly-stratified boundary layers, can be derived as invariant solutions defined under the Lie-group theory. A system truncated to the mean momentum and buoyancy equations is considered for this purpose. The study further suggests how similarity functions for the mean profiles are determined from the vertical fluxes, with a potential dependence on a measure of the anisotropy of the system. A time scale that is likely to characterize the transiency of a system is also identified as a non-dimensionalization factor. PubDate: 2024-04-30 DOI: 10.1007/s10546-024-00867-9

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Abstract: Abstract Taylor’s Frozen Turbulence Hypothesis (TH) is a critical assumption in turbulent theory and practice which allows time series of point measurements of turbulent variables to be translated to the spatial domain via the mean wind. Using a 3D array of fibre-optic distributed temperature sensing in the atmospheric surface layer over an idealized desert site we present a systematic investigation of the applicability of Taylor’s Hypothesis to atmospheric surface layer flows over a variety of conditions: unstable, near-neutral, and stable atmospheric stabilities; and multiple measurement heights between the surface and 3 m above ground level. Both spatially integrated and spatially scale-dependent eddy velocities are investigated by means of time-lagged streamwise two-point correlations and compared to the mean Eulerian wind. We find that eddies travel slower than predicted by TH at small spatial separations, as predicted by TH at separations typically between 5 and 16 m, and faster than predicted by TH at larger spatial separations. In unstable atmospheric conditions the spatial separation at which eddy velocity is larger than Eulerian velocity decreases with height. PubDate: 2024-04-30 DOI: 10.1007/s10546-024-00861-1

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Abstract: Abstract Wildland fire–atmosphere interaction generates complex turbulence patterns, organized across multiple scales, which inform fire-spread behaviour, firebrand transport, and smoke dispersion. Here, we utilize wavelet-based techniques to explore the characteristic temporal scales associated with coherent patterns in the measured temperature and the turbulent fluxes during a prescribed wind-driven (heading) surface fire beneath a forest canopy. We use temperature and velocity measurements from tower-mounted sonic anemometers at multiple heights. Patterns in the wavelet-based energy density of the measured temperature plotted on a time–frequency plane indicate the presence of fire-modulated ramp–cliff structures in the low-to-mid-frequency band (0.01–0.33 Hz), with mean ramp durations approximately 20% shorter and ramp slopes that are an order of magnitude higher compared to no-fire conditions. We then investigate heat- and momentum-flux events near the canopy top through a cross-wavelet coherence analysis. Briefly before the fire-front arrives at the tower base, momentum-flux events are relatively suppressed and turbulent fluxes are chiefly thermally-driven near the canopy top, owing to the tilting of the flame in the direction of the wind. Fire-induced heat-flux events comprising warm updrafts and cool downdrafts are coherent down to periods of a second, whereas ambient heat-flux events operate mainly at higher periods (above 17 s). Later, when the strongest temperature fluctuations are recorded near the surface, fire-induced heat-flux events occur intermittently at shorter scales and cool sweeps start being seen for periods ranging from 8 to 35 s near the canopy top, suggesting a diminishing influence of the flame and increasing background atmospheric variability thereat. The improved understanding of the characteristic time scales associated with fire-induced turbulence features, as the fire-front evolves, will help develop more reliable fire behaviour and scalar transport models. PubDate: 2024-04-18 DOI: 10.1007/s10546-024-00862-0

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Abstract: Abstract This study investigates flow variability at different scales and its effects on the dispersion of a passive scalar in a regular street network by means of direct numerical simulations (DNS), and compared to wind tunnel (WT) measurements. Specific scientific questions addressed include: (i) sources of variability in the flow at street-network scale, (ii) the effects of such variability on both puff and continuous localised releases, (iii) additional sources of uncertainty related to experimental setups and their consequences. The street network modelled here consists of an array of rectangular buildings arranged uniformly and with periodic horizontal boundary conditions. The flow is driven by a body force at an angle of 45 degrees relative to the streets in the network. Sources of passive scalars were located near ground level at three different types of locations: a short street, an intersection between streets and a long street. Flow variability is documented at different scales: small-scale intra-street variations linked with local flow topology; inter-street flow structure differences; street-network scale variability; and larger-scale spatial variations associated with above-canopy structures. Flow statistics and the dispersion behaviour of both continuous and short-duration (puff) releases of a passive scalar in the street network are analysed and compared with the results of wind-tunnel measurements. Results agree well with the experimental data for a source location in an intersection, especially for flow statistics and mean concentration profiles for continuous releases. Larger differences arise in the comparisons of puff releases. These differences are quantified by computing several puff parameters including time of arrival, travel time, rise and decay times. Reasons for the differences are discussed in relation to the underlying flow variability identified, differences between the DNS and WT setup and uncertainties in the experimental setup. Implications for the propagation of short-duration releases in real urban areas are discussed in the light of our findings. In particular, it is highlighted that in modelling singular events such as accidental releases, characterising uncertainties is more meaningful and useful than computing ensemble averages. PubDate: 2024-04-15 DOI: 10.1007/s10546-024-00863-z

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Abstract: Abstract A single-column turbulence model for stratified atmospheric boundary layer (ABL), which solves the transport equations of turbulence probability density function (PDF) using a Lagrangian stochastic modeling (LSM) approach, is proposed in this study. This study adopts previously developed stochastic differential equations (SDEs) for particle velocity and temperature and extends the LSM to simulate inhomogeneous turbulence. The proposed LSM is tested for its ability to fully simulate statistics of inhomogeneous stratified turbulence. In the model, particles evolve by SDEs, and turbulence statistics are calculated by averaging the properties of particles. The model provides a full representation of turbulence PDF and simulates turbulent transport without any modeling assumption. The model performance is evaluated against large-eddy simulation (LES) results in the simulations of convective and stable ABL cases. For the convective ABL, LSM realistically simulates the entrainment process with the temperature and heat flux profiles that closely match with LES. The joint PDF simulated by LSM reproduces a curved and highly skewed shape, and some distinct features, like the asymmetric distribution of vertical velocity and the separation of the PDF in the entrainment zone, are simulated. LSM also reproduces the entrainment enhancement by wind shear in the simulation of sheared convective ABL. The LSM simulation of stable ABL predicts realistic turbulence intensity and mean field profiles, where Gaussian-like PDFs are simulated both in LSM and LES. PubDate: 2024-04-06 DOI: 10.1007/s10546-023-00849-3