Optimizing the Determination of Roughness Parameters for Model Urban Canopies

We present an objective optimization procedure to determine the roughness parameters for very rough boundary-layer flow over model urban canopies. For neutral stratification the mean velocity profile above a model urban canopy is described by the logarithmic law together with the set of roughness parameters of displacement height d, roughness length \(z_0\), and friction velocity \(u_*\). Traditionally, values of these roughness parameters are obtained by fitting the logarithmic law through (all) the data points comprising the velocity profile. The new procedure generates unique velocity profiles from subsets or combinations of the data points of the original velocity profile, after which all possible profiles are examined. Each of the generated profiles is fitted to the logarithmic law for a sequence of values of d, with the representative value of d obtained from the minima of the summed least-squares errors for all the generated profiles. The representative values of \(z_0\) and \(u_*\) are identified by the peak in the bivariate histogram of \(z_0\) and \(u_*\). The methodology has been verified against laboratory datasets of flow above model urban canopies.     

Estimation of Surface-Layer Scaling Parameters in the Unstable Boundary Layer: Implications for Orographic Flow Speed-Up

A method is proposed for estimating the surface-layer depth \((z_s)\) and the friction velocity \((u_*)\) as a function of stability (here quantified by the Obukhov length, L) over the complete range of unstable flow regimes. This method extends that developed previously for stable conditions by Argaín et al. (Boundary-Layer Meteorol 130:15–28, 2009), but uses a qualitatively different approach. The method is specifically used to calculate the fractional speed-up \((\varDelta S)\) in flow over a ridge, although it is suitable for more general boundary-layer applications. The behaviour of \(z_s \left( L\right) \) and \(u_*\left( L\right) \) as a function of L is indirectly assessed via calculation of \(\varDelta S\left( L\right) \) using the linear model of Hunt et al. (Q J R Meteorol Soc 29:16–26, 1988) and its comparison with the field measurements reported in Coppin et al. (Boundary-Layer Meteorol 69:173–199, 1994) and with numerical simulations carried out using a non-linear numerical model, FLEX. The behaviour of \(\varDelta S\) estimated from the linear model is clearly improved when \(u_*\) is calculated using the method proposed here, confirming the importance of accounting for the dependences of \(z_s\left( L \right) \) and \(u_*\left( L \right) \) on L to better represent processes in the unstable boundary layer.     

Aerodynamic Properties of Rough Surfaces with High Aspect-Ratio Roughness Elements: Effect of Aspect Ratio and Arrangements

We examine the effect of varying roughness-element aspect ratio on the mean velocity distributions of turbulent flow over arrays of rectangular-prism-shaped elements. Large-eddy simulations (LES) in conjunction with a sharp-interface immersed boundary method are used to simulate spatially-growing turbulent boundary layers over these rough surfaces. Arrays of aligned and staggered rectangular roughness elements with aspect ratio >1 are considered. First the temporally- and spatially-averaged velocity profiles are used to illustrate the aspect-ratio effects. For aligned prisms, the roughness length (\(z_\mathrm{o}\)) and the friction velocity (\(u_*\)) increase initially with an increase in the roughness-element aspect ratio, until the values reach a plateau at a particular aspect ratio. The exact value of this aspect ratio depends on the coverage density. Further increase in the aspect ratio changes neither \(z_\mathrm{o}\), \(u_*\) nor the bulk flow above the roughness elements. For the staggered cases, \(z_\mathrm{o}\) and \(u_*\) continue to increase for the surface coverage density and the aspect ratios investigated. To model the flow response to variations in roughness aspect ratio, we turn to a previously developed phenomenological volumetric sheltering model (Yang et al., in J Fluid Mech 789:127–165, 2016), which was intended for low to moderate aspect-ratio roughness elements. Here, we extend this model to account for high aspect-ratio roughness elements. We find that for aligned cases, the model predicts strong mutual sheltering among the roughness elements, while the effect is much weaker for staggered cases. The model-predicted \(z_\mathrm{o}\) and \(u_*\) agree well with the LES results. Results show that the model, which takes explicit account of the mutual sheltering effects, provides a rapid and reliable prediction method of roughness effects in turbulent boundary-layer flows over arrays of rectangular-prism roughness elements.     

Scale Properties of Anisotropic and Isotropic Turbulence in the Urban Surface Layer

The scale properties of anisotropic and isotropic turbulence in the urban surface layer are investigated. A dimensionless anisotropic tensor is introduced and the turbulent tensor anisotropic coefficient, defined as C, where \(C = 3d_{3}\,+\,1 (d_{3}\) is the minimum eigenvalue of the tensor) is used to characterize the turbulence anisotropy or isotropy. Turbulence is isotropic when \(C \approx 1\), and anisotropic when \(C \ll 1\). Three-dimensional velocity data collected using a sonic anemometer are analyzed to obtain the anisotropic characteristics of atmospheric turbulence in the urban surface layer, and the tensor anisotropic coefficient of turbulent eddies at different spatial scales calculated. The analysis shows that C is strongly dependent on atmospheric stability \(\xi = (z-z_{\mathrm{d}})/L_{{\textit{MO}}}\), where z is the measurement height, \(z_{\mathrm{d}}\) is the displacement height, and \(L_{{\textit{MO}}}\) is the Obukhov length. The turbulence at a specific scale in unstable conditions (i.e., \(\xi < 0\)) is closer to isotropic than that at the same scale under stable conditions. The maximum isotropic scale of turbulence is determined based on the characteristics of the power spectrum in three directions. Turbulence does not behave isotropically when the eddy scale is greater than the maximum isotropic scale, whereas it is horizontally isotropic at relatively large scales. The maximum isotropic scale of turbulence is compared to the outer scale of temperature, which is obtained by fitting the temperature fluctuation spectrum using the von Karman turbulent model. The results show that the outer scale of temperature is greater than the maximum isotropic scale of turbulence.     

Estimating Sediment Mass Fluxes on Surfaces Sheltered by Live Vegetation

We present a simple model based on already existing and widely used equations for estimating particle mass fluxes on surfaces sheltered by live vegetation. Wind-tunnel measurements of vertical profiles of mass flux in three different dense live plant canopies, and as a function of the spatially averaged skin friction velocity \({u_{\tau }}'\), provide the baseline set of data. For the bare-sand surface, the total mass flux Q shows the typical \(b({u_\tau }' - {u_{\tau t}}')^{3 }\) increase with increasing skin friction velocity \({u_{\tau }}'\), where b is a constant and \({u_{\tau t}}'\) is the threshold at the onset of particle erosion. Similar relations, however, with different values for b and \({u_{\tau t}}'\) compared to the bare-sand surface were found for experiments with 5.25 and 24.5 plants \(\hbox {m}^{-2}\) and can be explained by the spatial variations of \(u_{\tau }\) for the canopy cases. Based on the resulting parameters b and \({u_{\tau t}}'\), which are found to be functions of the roughness density \(\lambda \), we present a final simple relation \(Q(\lambda ,\, {u_{\tau }}')\) used for estimating the total mass flux for surfaces sheltered by live vegetation.     

Scaling of Wall-Normal Turbulence Intensity and Vertical Eddy Structures in the Atmospheric Surface Layer

Adequate high-quality data on three-dimensional velocities in the atmospheric surface layer (height \(\delta \)) were acquired in the field at the Qingtu Lake Observation Array. The measurement range occupies nearly the entire logarithmic layer from approximately \(0.006\delta \)–\(0.2\delta \). The turbulence intensity and eddy structures of the velocity fluctuations in the logarithmic region were primarily analyzed, and their variations in the z (wall-normal) direction were revealed. The primary finding was that the turbulent intensity of wall-normal velocity fluctuations exhibits a sharp upswing in the logarithmic region, which differs from classic scaling law and laboratory results. The upswing of the wall-normal turbulence intensity in the logarithmic region is deemed to be linear based on an ensemble of 20 sets of data. In addition, the wall-normal extent of the correlated structures and wall-normal spectra were compared to low Reynolds number results in the laboratory.     

Katabatic Flow: A Closed-Form Solution with Spatially-Varying Eddy Diffusivities

The Nieuwstadt closed-form solution for the stationary Ekman layer is generalized for katabatic flows within the conceptual framework of the Prandtl model. The proposed solution is valid for spatially-varying eddy viscosity and diffusivity (O’Brien type) and constant Prandtl number (Pr). Variations in the velocity and buoyancy profiles are discussed as a function of the dimensionless model parameters \(z_0 \equiv \hat{z}_0 \hat{N}^2 Pr \sin {(\alpha )} |\hat{b}_\mathrm{s} |^{-1}\) and \(\lambda \equiv \hat{u}_{\mathrm{ref}}\hat{N} \sqrt{Pr} |\hat{b}_\mathrm{s} |^{-1}\), where \(\hat{z}_0\) is the hydrodynamic roughness length, \(\hat{N}\) is the Brunt-Väisälä frequency, \(\alpha \) is the surface sloping angle, \(\hat{b}_\mathrm{s}\) is the imposed surface buoyancy, and \(\hat{u}_{\mathrm{ref}}\) is a reference velocity scale used to define eddy diffusivities. Velocity and buoyancy profiles show significant variations in both phase and amplitude of extrema with respect to the classic constant \(\textit{K}\) model and with respect to a recent approximate analytic solution based on the Wentzel-Kramers-Brillouin theory. Near-wall regions are characterized by relatively stronger surface momentum and buoyancy gradients, whose magnitude is proportional to \(z_0\) and to \(\lambda \). In addition, slope-parallel momentum and buoyancy fluxes are reduced, the low-level jet is further displaced toward the wall, and its peak velocity depends on both \(z_0\) and \(\lambda \).     

On the Nature of the Transition Between Roll and Cellular Organization in the Convective Boundary Layer

Both observational and numerical studies of the convective boundary layer (CBL) have demonstrated that when surface heat fluxes are small and mean wind shear is strong, convective updrafts tend to organize into horizontal rolls aligned within 10–20\(^\circ \) of the geostrophic wind direction. However, under large surface heat fluxes and weak to negligible shear, convection tends to organize into open cells, similar to turbulent Rayleigh-Bénard convection. Using a suite of 14 large-eddy simulations (LES) spanning a range of \(-z_i/L\) between zero (neutral) and 1041 (highly convective), where \(z_i\) is the CBL depth and L is the Obukhov length, the transition between roll- and cellular-type convection is investigated systematically for the first time using LES. Mean vertical profiles including velocity variances and turbulent transport efficiencies, as well the “roll factor,” which characterizes the rotational symmetry of the vertical velocity field, indicate the transition occurs gradually over a range of \(-z_i/L\); however, the most significant changes in vertical profiles and CBL organization occur from near-neutral conditions up to about \(-z_i/L \approx \) 15–20. Turbulent transport efficiencies and quadrant analysis are used to characterize the turbulent transport of momentum and heat with increasing \(-z_i/L\). It is found that turbulence transports heat efficiently from weakly to highly convective conditions; however, turbulent momentum transport becomes increasingly inefficient as \(-z_i/L\) increases.     

Characteristics of Turbulent Airflow Deduced from Rapid Surface Thermal Fluctuations: An Infrared Surface Anemometer

The intermittent nature of turbulent airflow interacting with the surface is readily observable in fluctuations of the surface temperature resulting from the thermal imprints of eddies sweeping the surface. Rapid infrared thermography has recently been used to quantify characteristics of the near-surface turbulent airflow interacting with the evaporating surfaces. We aim to extend this technique by using single-point rapid infrared measurements to quantify properties of a turbulent flow, including surface exchange processes, with a view towards the development of an infrared surface anemometer. The parameters for the surface-eddy renewal (\(\alpha \) and \(\beta )\) are inferred from infrared measurements of a single-point on the surface of a heat plate placed in a wind tunnel with prescribed wind speeds and constant mean temperatures of the surface. Thermally-deduced parameters are in agreement with values obtained from standard three-dimensional ultrasonic anemometer measurements close to the plate surface (e.g., \(\alpha = 3\) and \(\beta = 1/26~\hbox {(ms)}^{-1}\) for the infrared, and \(\alpha = 3\) and \(\beta = 1/19~\hbox {(ms)}^{-1}\) for the sonic-anemometer measurements). The infrared-based turbulence parameters provide new insights into the role of surface temperature and buoyancy on the inherent characteristics of interacting eddies. The link between the eddy-spectrum shape parameter \(\alpha \) and the infrared window size representing the infrared field of view is investigated. The results resemble the effect of the sampling height above the ground in sonic anemometer measurements, which enables the detection of larger eddies with higher values of \(\alpha \). The physical basis and tests of the proposed method support the potential for remote quantification of the near-surface momentum field, as well as scalar-flux measurements in the immediate vicinity of the surface.     

Simplification and Validation of a Spectral-Tensor Model for Turbulence Including Atmospheric Stability

A spectral-tensor model of non-neutral, atmospheric-boundary-layer turbulence is evaluated using Eulerian statistics from single-point measurements of the wind speed and temperature at heights up to 100 m, assuming constant vertical gradients of mean wind speed and temperature. The model has been previously described in terms of the dissipation rate \(\epsilon \), the length scale of energy-containing eddies \(\mathcal {L}\), a turbulence anisotropy parameter \(\varGamma \), the Richardson number Ri, and the normalized rate of destruction of temperature variance \(\eta _\theta \equiv \epsilon _\theta /\epsilon \). Here, the latter two parameters are collapsed into a single atmospheric stability parameter z / L using Monin–Obukhov similarity theory, where z is the height above the Earth’s surface, and L is the Obukhov length corresponding to \(\{Ri,\eta _\theta \}\). Model outputs of the one-dimensional velocity spectra, as well as cospectra of the streamwise and/or vertical velocity components, and/or temperature, and cross-spectra for the spatial separation of all three velocity components and temperature, are compared with measurements. As a function of the four model parameters, spectra and cospectra are reproduced quite well, but horizontal temperature fluxes are slightly underestimated in stable conditions. In moderately unstable stratification, our model reproduces spectra only up to a scale \(\sim \) 1 km. The model also overestimates coherences for vertical separations, but is less severe in unstable than in stable cases.     

Conditionally Averaged Large-Scale Motions in the Neutral Atmospheric Boundary Layer: Insights for Aeolian Processes

Aeolian erosion of flat, arid landscapes is induced (and sustained) by the aerodynamic surface stress imposed by flow in the atmospheric surface layer. Conceptual models typically indicate that sediment mass flux, Q (via saltation or drift), scales with imposed aerodynamic stress raised to some exponent, n, where \(n > 1\). This scaling demonstrates the importance of turbulent fluctuations in driving aeolian processes. In order to illustrate the importance of surface-stress intermittency in aeolian processes, and to elucidate the role of turbulence, conditional averaging predicated on aerodynamic surface stress has been used within large-eddy simulation of atmospheric boundary-layer flow over an arid, flat landscape. The conditional-sampling thresholds are defined based on probability distribution functions of surface stress. The simulations have been performed for a computational domain with \(\approx 25 H\) streamwise extent, where H is the prescribed depth of the neutrally-stratified boundary layer. Thus, the full hierarchy of spatial scales are captured, from surface-layer turbulence to large- and very-large-scale outer-layer coherent motions. Spectrograms are used to support this argument, and also to illustrate how turbulent energy is distributed across wavelengths with elevation. Conditional averaging provides an ensemble-mean visualization of flow structures responsible for erosion ‘events’. Results indicate that surface-stress peaks are associated with the passage of inclined, high-momentum regions flanked by adjacent low-momentum regions. Fluid in the interfacial shear layers between these adjacent quasi-uniform momentum regions exhibits high streamwise and vertical vorticity.     

Global Intermittency and Collapsing Turbulence in the Stratified Planetary Boundary Layer

Direct numerical simulation of the turbulent Ekman layer over a smooth wall is used to investigate bulk properties of a planetary boundary layer under stable stratification. Our simplified configuration depends on two non-dimensional parameters: a Richardson number characterizing the stratification and a Reynolds number characterizing the turbulence scale separation. This simplified configuration is sufficient to reproduce global intermittency, a turbulence collapse, and the decoupling of the surface from the outer region of the boundary layer. Global intermittency appears even in the absence of local perturbations at the surface; the only requirement is that large-scale structures several times wider than the boundary-layer height have enough space to develop. Analysis of the mean velocity, turbulence kinetic energy, and external intermittency is used to investigate the large-scale structures and corresponding differences between stably stratified Ekman flow and channel flow. Both configurations show a similar transition to the turbulence collapse, overshoot of turbulence kinetic energy, and spectral properties. Differences in the outer region resulting from the rotation of the system lead, however, to the generation of enstrophy in the non-turbulent patches of the Ekman flow. The coefficient of the stability correction function from Monin–Obukhov similarity theory is estimated as \(\beta \approx 5.7\) in agreement with atmospheric observations, theoretical considerations, and results from stably stratified channel flows. Our results demonstrate the applicability of this set-up to atmospheric problems despite the intermediate Reynolds number achieved in our simulations.     

An Efficient Non-iterative Bulk Parametrization of Surface Fluxes for Stable Atmospheric Conditions Over Polar Sea-Ice

In climate and weather prediction models the near-surface turbulent fluxes of heat and momentum and related transfer coefficients are usually parametrized on the basis of Monin–Obukhov similarity theory (MOST). To avoid iteration, required for the numerical solution of the MOST equations, many models apply parametrizations of the transfer coefficients based on an approach relating these coefficients to the bulk Richardson number \(Ri_{b}\). However, the parametrizations that are presently used in most climate models are valid only for weaker stability and larger surface roughnesses than those documented during the Surface Heat Budget of the Arctic Ocean campaign (SHEBA). The latter delivered a well-accepted set of turbulence data in the stable surface layer over polar sea-ice. Using stability functions based on the SHEBA data, we solve the MOST equations applying a new semi-analytic approach that results in transfer coefficients as a function of \(Ri_{b}\) and roughness lengths for momentum and heat. It is shown that the new coefficients reproduce the coefficients obtained by the numerical iterative method with a good accuracy in the most relevant range of stability and roughness lengths. For small \(Ri_{b}\), the new bulk transfer coefficients are similar to the traditional coefficients, but for large \(Ri_{b}\) they are much smaller than currently used coefficients. Finally, a possible adjustment of the latter and the implementation of the new proposed parametrizations in models are discussed.     

Experimental Investigation of Turbulent Momentum Transfer in a Neutral Boundary Layer over a Rough Surface

The turbulent characteristics of the neutral boundary layer developing over rough surfaces are not well predicted with operational weather-forecasting models. The problem is attributed to inadequate mixing-length models, to the anisotropy of the flow and to a lack of controlled experimental data against which to validate numerical studies. Therefore, in order to address directly the modelling difficulties for the development of a neutral boundary layer over rough surfaces, and to investigate the turbulent momentum transfer of such a layer, a set of hydraulic flume experiments were carried out. In the experiments, the mean and turbulent quantities were measured by a particle image velocimetry (PIV) technique. The measured velocity variances and fluxes \({(\overline{{u_{i}^{\prime}}{u_{j}^{\prime}}})}\) in longitudinal vertical planes allowed the vertical and longitudinal gradients (?/?z and ?/?x) of the mean and turbulent quantities (fluxes, variances and third-order moments) to be evaluated and the terms of the evolution equations for ?e/?t, \({\partial \overline{u^{\prime 2}}/\partial t}\), \({\partial \overline{w^{\prime 2}}/\partial t}\) and \({\partial \overline{{u^{\prime}}{w^{\prime}}}/\partial t}\) to be quantified, where e is the turbulent kinetic energy. The results show that the pressure-correlation terms allow the turbulent energy to be transferred equitably from \({\overline{{u^{\prime}}^{2}}}\) to \({\overline{{w^{\prime}}^{2}}}\). It appears that the repartition between the constitutive terms of the budget of e, \({\overline{{u^{\prime}}^{2}}}\), \({\overline{{w^{\prime}}^{2}}}\) and \({\overline{{u^{\prime}}{w^{\prime}}}}\) is not significantly affected by the development of the rough neutral boundary layer. For the whole evolution, the transfers of energy are governed by the same terms that are also very similar to the smooth-wall case. The PIV measurements also allowed the spatial integral scales to be computed directly and to be compared with the dissipative and mixing length scales, which were also computed from the data.     

High-Resolution Vertical Profile Measurements for Carbon Dioxide and Water Vapour Concentrations Within and Above Crop Canopies

We present a portable elevator-based facility for measuring \(\hbox {CO}_{2}\), water vapour, temperature and wind-speed profiles between the soil surface and the atmospheric surface layer above crop canopies. The end of a tube connected to a closed-path gas analyzer is continuously moved up and down over the profile range (in our case, approximately 2 m) while concentrations are logged at a frequency of \(20 \hbox { s}^{-1}\). Using campaign measurements in winter wheat, winter barley and a catch crop mixture (spring 2015 to autumn 2016) during different stages of crop development and different times of the day, we demonstrate a simple approach to correct for time lags, and the resulting profiles of 30-min mean mole fractions of \(\hbox {CO}_{2}\) and \(\hbox {H}_{2}\hbox {O}\) over height increments of 0.025 m. The profiles clearly show the effects of soil respiration and photosynthetic carbon assimilation, varying both during the diurnal cycle and during the growing season. Profiles of temperature and wind speed are based on a ventilated finewire thermocouple and a hot-wire anemometer, respectively. Measurements over bare soil and a short plant canopy were analyzed in the framework of Monin–Obukhov similarity theory to check the validity of the measurements and raw-data-processing approach. Derived fluxes of \(\hbox {CO}_{2}\), latent and sensible heat and momentum show good agreement with eddy-covariance measurements.     

Turbulence in Continental Stratocumulus,Part I: External Forcings and Turbulence Structures

Comprehensive, ground-based observations from the US Department of Energy Atmospheric Radiation Measurements program Southern Great Plains site are used to study the variability of turbulence forcings and cloud-scale turbulence structures in a continental stratocumulus cloud. The turbulence observations are made from an upward facing cloud (35 GHz) Doppler radar. Cloud base and liquid water path are characterized using a lidar at the surface and a microwave radiometer. The turbulence characterizations are compared and contrasted with those observed in marine stratocumulus clouds. During the 16-h observation period used in this study the cloud-base and cloud-top heights evolve with time and changes in liquid water path observed by the radiometer are consistent with variations in cloud depth. Unlike marine stratocumulus clouds, a diurnal cycle of cloud thickness and liquid water path is not observed. The observed surface latent, sensible, and virtual sensible heat fluxes and the radiative fluxes exhibit a diurnal cycle with values increasing from sunrise to afternoon and decreasing afterwards. During the night, the sensible heat, virtual sensible heat and the net radiative fluxes at the surface are slightly negative. Solar radiative heating prevails in the cloud layer during the day and strong radiative cooling exists at cloud top even during the day. Unlike marine stratocumulus, surface heating described by the convective velocity scale \(W_\mathrm{s}^{*}\) and cloud-top cooling described by \(W_\mathrm{r}^{*}\) are both important in driving the in-cloud turbulence during the day, whereas cloud-top cooling is the exclusive contributor during the night. The combined \(W_\mathrm{s}^{*}\) and \(W_\mathrm{r}^{*}\) (the total velocity scale \(W_\mathrm{t}^{*})\) provides a useful way to track the evolution of the turbulence structure in the cloud. The variance of the radar-measured radial velocity, which is related to resolved turbulence, follows the diurnal cycle and is consistent with the total velocity scale \(W_\mathrm{t}^{*}\) variations. It is higher during the day and lower during the night, which is contrary to that in marine stratocumulus. The \(W_\mathrm{t}^{*}\) values are lowest around sunset when the radiative cooling is also small due to upper-level clouds observed above the low-level stratus. The vertical distribution of the variance results from the surface heating during the day and cloud-top cooling during the night. The squared spectrum width, which is related to turbulence structures within the radar sampling volume (unresolved turbulence) also follows the diurnal cycle. Its vertical distribution indicates that the unresolved turbulence more closely relates to the processes near cloud top. Turbulence in the cloud requires about an hour to respond to the external forcings of surface heating and cloud-top radiative cooling. Positive skewness prevails during the day and negative skewness prevails at night with a sharp transition around sunset. Resolved turbulence dominates near cloud base whereas unresolved turbulence dominates near cloud top. The turbulence characteristics and variability defined in this study can be used to evaluate the time evolution of turbulence structures in large eddy simulation forced by surface and cloud-top radiative forcings.     

Coamps<Superscript>®</Superscript>-Les: Model Evaluation and Analysis of Second-and Third-Moment Vertical Velocity Budgets

The Naval Research Laboratory Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS^®) has been extended to perform as a large-eddy simulation (LES) model. It has been validated with a series of boundary-layer experiments spanning a range of cloud nighttime, and includes a nighttime stratocumulus case, a trade wind cumulus layer, shallow cumulus convection over land, and a mixed regime consisting of cumulus clouds under broken stratocumulus. COAMPS-LES results are in good agreement with other models for all the cases simulated. Exact numerical budgets for the vertical velocity second\((\overline{w^{'2}})\) and third moment\((\overline{w^{'3}})\) have been derived for the stratocumulus and trade wind cumulus cases. For the\(\overline{w^{'3}}\) budget in the stratocumulus, the buoyancy contribution from the updraughts and downdraughts largely cancel each other due to their similar magnitudes but opposite signs. In contrast, for the cumulus layer, the negative buoyancy contribution from the environmental downdraughts is negligible and the positive contribution from the updraughts completely dominates due to the conditional instability in the environment. As a result,\(\overline{w^{'3}}\) is significantly larger in the cumulus than in the stratocumulus layer.     

Spatially-Averaged Temperature Structure Parameter Over a Heterogeneous Surface Measured by an Unmanned Aerial Vehicle

The structure parameter of temperature, \({C_{T}^{2}}\) , in the lower convective boundary layer was measured using the unmanned mini aerial vehicle M²AV. The measurements were carried out on two hot summer days in July 2010 over a heterogeneous land surface around the boundary-layer field site of the Lindenberg Meteorological Observatory—Richard-Aßmann-Observatory of the German Meteorological Service. The spatial series of \({C_{T}^{2}}\) showed considerable variability along the flight path that was caused by both temporal variations and surface heterogeneity. Comparison of the aircraft data with \({C_{T}^{2}}\) values derived from tower-based in situ turbulence measurements showed good agreement with respect to the diurnal variability. The decrease of \({C_{T}^{2}}\) with height as predicted by free-convection scaling could be confirmed for the morning and afternoon flights while the flights around noon suggest a different behaviour.     

Water-Channel Estimation of Eulerian and Lagrangian Time Scales of the Turbulence in Idealized Two-Dimensional Urban Canopies

Lagrangian and Eulerian statistics are obtained from a water-channel experiment of an idealized two-dimensional urban canopy flow in neutral conditions. The objective is to quantify the Eulerian \((T^{\mathrm{E}})\) and Lagrangian \((T^{\mathrm{L}})\) time scales of the turbulence above the canopy layer as well as to investigate their dependence on the aspect ratio of the canopy, AR, as the latter is the ratio of the width (W) to the height (H) of the canyon. Experiments are also conducted for the case of flat terrain, which can be thought of as equivalent to a classical one-directional shear flow. The values found for the Eulerian time scales on flat terrain are in agreement with previous numerical results found in the literature. It is found that both the streamwise and vertical components of the Lagrangian time scale, \(T_\mathrm{u}^\mathrm{L} \) and \(T_\mathrm{w}^\mathrm{L} \), follow Raupach’s linear law within the constant-flux layer. The same holds true for \(T_\mathrm{w}^\mathrm{L} \) in both the canopies analyzed \((AR= 1\) and \(AR= 2\)) and also for \(T_\mathrm{u}^\mathrm{L} \) when \(AR = 1\). In contrast, for \(AR = 2\), \(T_\mathrm{u}^\mathrm{L} \) follows Raupach’s law only above \(z=2H\). Below that level, \(T_\mathrm{u}^\mathrm{L} \) is nearly constant with height, showing at \(z=H\) a value approximately one order of magnitude greater than that found for \(AR = 1\). It is shown that the assumption usually adopted for flat terrain, that \(\beta =T^{\mathrm{L}}/T^{\mathrm{E}}\) is proportional to the inverse of the turbulence intensity, also holds true even for the canopy flow in the constant-flux layer. In particular, \(\gamma /i_\mathrm{u} \) fits well \(\beta _\mathrm{u} =T_\mathrm{u}^\mathrm{L} /T_\mathrm{u}^\mathrm{E} \) in both the configurations by choosing \(\gamma \) to be 0.35 (here, \(i_\mathrm{u} =\sigma _\mathrm{u} / \bar{u} \), where \(\bar{u} \) and \(\sigma _\mathrm{u} \) are the mean and the root-mean-square of the streamwise velocity component, respectively). On the other hand, \(\beta _\mathrm{w} =T_\mathrm{w}^\mathrm{L} /T_\mathrm{w}^\mathrm{E} \) follows approximately \(\gamma /i_\mathrm{w} =0.65/\left( {\sigma _\mathrm{w} /\bar{u} } \right) \) for \(z > 2H\), irrespective of the AR value. The second main objective is to estimate other parameters of interest in dispersion studies, such as the eddy diffusivity of momentum \((K_\mathrm{{T}})\) and the Kolmogorov constant \((C_0)\). It is found that \(C_0\) depends appreciably on the velocity component both for the flat terrain and canopy flow, even though for the latter case it is insensitive to AR values. In all the three experimental configurations analyzed here, \(K_\mathrm{{T}}\) shows an overall linear growth with height in agreement with the linear trend predicted by Prandtl’s theory.