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As a consequence of the rapid growth of the globally installed offshore wind energy capacity, the size of individual wind farms is increasing. This poses a challenge to models that predict energy production. For instance, the current generation of wake models has mostly been calibrated on existing wind farms of much smaller size. This work analyzes annual energy production and wake losses for future, multi-gigawatt wind farms with atmospheric large-eddy simulation. To that end, 1 year of actual weather has been simulated for a suite of hypothetical 4 GW offshore wind farm scenarios. The scenarios differ in terms of applied turbine type, installed capacity density, and layout. The results suggest that production numbers increase significantly when the rated power of the individual turbines is larger while keeping the total installed capacity the same. Even for turbine types with similar rated power but slightly different power curves, significant differences in production were found. Although wind speed was identified as the most dominant factor determining the aerodynamic losses, a clear impact of atmospheric stability and boundary layer height has been identified. By analyzing losses of the first-row turbines, the yearly average global-blockage effect is estimated to between 2 and 3 %, but it can reach levels over 10 % for stably stratified conditions and wind speeds around 8 m s−1. Using a high-fidelity modeling technique, the present work provides insights into the performance of future, multi-gigawatt wind farms for a full year of realistic weather conditions., Energie and Industrie, Atmospheric Remote Sensing

This study investigates how wind shear and momentum fluxes in the surface- and boundary layer vary across wind and cloud regimes. We use a 9-year-long data set from the Cabauw observatory complemented by (8.2 × 8.2 (Formula presented.)) daily Large Eddy Simulation (LES) hindcasts. An automated algorithm classifies observed and simulated days into different cloud regimes: (a) clear-sky days, (b) days with shallow convective clouds rooted in the surface layer, with two ranges of cloud cover, and (c) non-convective cloud days. Categorized days in observations and LES do not always match, particularly the number of non-convective cloud days are underestimated in the LES, which likes to develop convection. However, the climatology and diurnal cycle of winds for each regime are very similar in LES and observations, strengthening our confidence in LES’ skill to reproduce certain clouds for certain atmospheric states. Along-wind momentum flux profiles are similar across all regimes, but large cloud cover (convective and non-convective) days have larger total momentum flux distributed over a deeper layer, with up to 30% of the surface flux still present near cloud base. The clear-sky and especially shallow cumulus regime with low cloud cover have notably larger crosswind momentum fluxes in the boundary layer. Surface-layer wind shear at daytime is smallest in the shallow cumulus regimes, having deeper boundary layers and a steady increase in surface layer wind speed during daytime. Compared to clear-sky days at a similar stability, convective cloud regimes have smaller surface-layer wind shear and larger surface friction than estimated by Monin-Obukhov Similarity Theory., Atmospheric Remote Sensing

This study investigates how wind shear and momentum fluxes in the surface- and boundary layer vary across wind and cloud regimes. We use a 9-year-long data set from the Cabauw observatory complemented by (8.2 × 8.2 (Formula presented.)) daily Large Eddy Simulation (LES) hindcasts. An automated algorithm classifies observed and simulated days into different cloud regimes: (a) clear-sky days, (b) days with shallow convective clouds rooted in the surface layer, with two ranges of cloud cover, and (c) non-convective cloud days. Categorized days in observations and LES do not always match, particularly the number of non-convective cloud days are underestimated in the LES, which likes to develop convection. However, the climatology and diurnal cycle of winds for each regime are very similar in LES and observations, strengthening our confidence in LES’ skill to reproduce certain clouds for certain atmospheric states. Along-wind momentum flux profiles are similar across all regimes, but large cloud cover (convective and non-convective) days have larger total momentum flux distributed over a deeper layer, with up to 30% of the surface flux still present near cloud base. The clear-sky and especially shallow cumulus regime with low cloud cover have notably larger crosswind momentum fluxes in the boundary layer. Surface-layer wind shear at daytime is smallest in the shallow cumulus regimes, having deeper boundary layers and a steady increase in surface layer wind speed during daytime. Compared to clear-sky days at a similar stability, convective cloud regimes have smaller surface-layer wind shear and larger surface friction than estimated by Monin-Obukhov Similarity Theory., Atmospheric Remote Sensing

High-resolution large-eddy simulations of the Antarctic very stable boundary layer reveal a mechanism for systematic and periodic intermittent bursting. A nonbursting state with a boundary layer height of just 3 m is alternated by a bursting state with a height of ≈5 m. The bursts result from unstable wave growth triggered by a shear-generated Kelvin–Helmholtz instability, as confirmed by linear stability analysis. The shear at the top of the boundary layer is built up by two processes. The upper, quasi-laminar layer accelerates due to the combined effect of the pressure force and rotation by the Coriolis force, while the lower layer decelerates by turbulent friction. During the burst, this shear is eroded and the initial cause of the instability is removed. Subsequently, the interfacial shear builds up again, causing the entire sequence to repeat itself with a time scale of ≈10 min. Despite the clear intermittent bursting, the overall change of the mean wind profile is remarkably small during the cycle. This enables such a fast erosion and recovery of the shear. This mechanism for cyclic bursting is remarkably similar to the mechanism hypothesized by Businger in 1973, with one key difference. Whereas Businger proposes that the flow acceleration in the upper layer results from downward turbulent transfer of high-momentum flow, the current results indicate no turbulent activity in the upper layer, hence requiring another source of momentum. Finally, it would be interesting to construct a climatology of shear-generated intermittency in relation to large-scale conditions to assess the generality of this Businger mechanism., Atmospheric Remote Sensing

This study investigated the surface temperature, air temperature and mean radiant temperature inside an idealized 2D street geometry during daytime. The goal was to unravel the relative impact of radiative transfer, heat conduction and ventilation to the urban heat budget. A building-resolving simulation model has been used, which represents these processes at a 1 m spatial resolution. Different combinations of the canyon height to width ratio (H/W) and physical mechanisms were investigated. Shortwave radiation is the main source of energy, and for small H/W can be higher at the canyon ground level compared to flat terrain due to multiple reflections. The longwave trapping effect has the second largest contribution and becomes relatively more important with increasing H/W ratio. The influence of the interior building temperature is small. Surface temperature and mean radiant temperature are closely related, since both are largely controlled by radiative properties. No straightforward relation was found between surface temperature and air temperature, since air temperature is dependent on the competing mechanisms of forced and natural convection. A small increase in air temperature inside the canyon was observed compared to the ambient temperature above roof level. The inclusion of all key physical processes in high detail resulted in large computational requirements. If multiple reflections by the building facades are small, the more traditional, yet much simpler view factor approach will strongly reduce the computational costs as compared to the Monte Carlo technique. The influence of using the view factors on the results must be investigated., Atmospheric Remote Sensing, ChemE/Transport Phenomena

High-resolution large-eddy simulations of the Antarctic very stable boundary layer reveal a mechanism for systematic and periodic intermittent bursting. A nonbursting state with a boundary layer height of just 3 m is alternated by a bursting state with a height of ≈5 m. The bursts result from unstable wave growth triggered by a shear-generated Kelvin–Helmholtz instability, as confirmed by linear stability analysis. The shear at the top of the boundary layer is built up by two processes. The upper, quasi-laminar layer accelerates due to the combined effect of the pressure force and rotation by the Coriolis force, while the lower layer decelerates by turbulent friction. During the burst, this shear is eroded and the initial cause of the instability is removed. Subsequently, the interfacial shear builds up again, causing the entire sequence to repeat itself with a time scale of ≈10 min. Despite the clear intermittent bursting, the overall change of the mean wind profile is remarkably small during the cycle. This enables such a fast erosion and recovery of the shear. This mechanism for cyclic bursting is remarkably similar to the mechanism hypothesized by Businger in 1973, with one key difference. Whereas Businger proposes that the flow acceleration in the upper layer results from downward turbulent transfer of high-momentum flow, the current results indicate no turbulent activity in the upper layer, hence requiring another source of momentum. Finally, it would be interesting to construct a climatology of shear-generated intermittency in relation to large-scale conditions to assess the generality of this Businger mechanism., Atmospheric Remote Sensing

This study investigated the surface temperature, air temperature and mean radiant temperature inside an idealized 2D street geometry during daytime. The goal was to unravel the relative impact of radiative transfer, heat conduction and ventilation to the urban heat budget. A building-resolving simulation model has been used, which represents these processes at a 1 m spatial resolution. Different combinations of the canyon height to width ratio (H/W) and physical mechanisms were investigated. Shortwave radiation is the main source of energy, and for small H/W can be higher at the canyon ground level compared to flat terrain due to multiple reflections. The longwave trapping effect has the second largest contribution and becomes relatively more important with increasing H/W ratio. The influence of the interior building temperature is small. Surface temperature and mean radiant temperature are closely related, since both are largely controlled by radiative properties. No straightforward relation was found between surface temperature and air temperature, since air temperature is dependent on the competing mechanisms of forced and natural convection. A small increase in air temperature inside the canyon was observed compared to the ambient temperature above roof level. The inclusion of all key physical processes in high detail resulted in large computational requirements. If multiple reflections by the building facades are small, the more traditional, yet much simpler view factor approach will strongly reduce the computational costs as compared to the Monte Carlo technique. The influence of using the view factors on the results must be investigated., Atmospheric Remote Sensing, ChemE/Transport Phenomena

Observations of two typical contrasting weakly stable and very stable boundary layers from the winter at Dome C station, Antarctica, are used as a benchmark for two centimetre-scale-resolution large-eddy simulations. By taking the Antarctic winter, the effects of the diurnal cycle are eliminated, enabling the study of the long-lived steady stable boundary layer. With its homogeneous, flat snow surface, and extreme stabilities, the location is a natural laboratory for studies on the long-lived stable boundary layer. The two simulations differ only in the imposed geostrophic wind speed, which is identified as the main deciding factor for the resulting regime. In general, a good correspondence is found between the observed and simulated profiles of mean wind speed and temperature. Discrepancies in the temperature profiles are likely due to the exclusion of radiative transfer in the current simulations. The extreme stabilities result in a considerable contrast between the stable boundary layer at the Dome C site and that found at typical mid-latitudes. The boundary-layer height is found to range from approximately 50m to just 5m in the most extreme case. Remarkably, heating of the boundary layer by subsidence may result in thermal equilibrium of the boundary layer in which the associated heating is balanced by the turbulent cooling towards the surface. Using centimetre-scale resolutions, accurate large-eddy simulations of the extreme stabilities encountered in Antarctica appear to be possible. However, future simulations should aim to include radiative transfer and sub-surface heat transport to increase the degree of realism of these types of simulations., Atmospheric Remote Sensing

Observations of two typical contrasting weakly stable and very stable boundary layers from the winter at Dome C station, Antarctica, are used as a benchmark for two centimetre-scale-resolution large-eddy simulations. By taking the Antarctic winter, the effects of the diurnal cycle are eliminated, enabling the study of the long-lived steady stable boundary layer. With its homogeneous, flat snow surface, and extreme stabilities, the location is a natural laboratory for studies on the long-lived stable boundary layer. The two simulations differ only in the imposed geostrophic wind speed, which is identified as the main deciding factor for the resulting regime. In general, a good correspondence is found between the observed and simulated profiles of mean wind speed and temperature. Discrepancies in the temperature profiles are likely due to the exclusion of radiative transfer in the current simulations. The extreme stabilities result in a considerable contrast between the stable boundary layer at the Dome C site and that found at typical mid-latitudes. The boundary-layer height is found to range from approximately 50m to just 5m in the most extreme case. Remarkably, heating of the boundary layer by subsidence may result in thermal equilibrium of the boundary layer in which the associated heating is balanced by the turbulent cooling towards the surface. Using centimetre-scale resolutions, accurate large-eddy simulations of the extreme stabilities encountered in Antarctica appear to be possible. However, future simulations should aim to include radiative transfer and sub-surface heat transport to increase the degree of realism of these types of simulations., Atmospheric Remote Sensing

Simultaneous particle-image velocimetry and laser-induced fluorescence combined with large-eddy simulations are used to investigate the flow and pollutant dispersion behaviour in a rural-to-urban roughness transition. The urban roughness is characterized by an array of cubical obstacles in an aligned arrangement. A plane fence is added one obstacle height h upstream of the urban roughness elements, with three different fence heights considered. A smooth-wall turbulent boundary layer with a depth of 10h is used as the approaching flow, and a passive tracer is released from a uniform line source 1h upstream of the fence. A shear layer is formed at the top of the fence, which increases in strength for the higher fence cases, resulting in a deeper internal boundary layer (IBL). It is found that the mean flow for the rural-to-urban transition can be described by means of a mixing-length model provided that the transitional effects are accounted for. The mixing-length formulation for sparse urban canopies, as found in the literature, is extended to take into account the blockage effect in dense canopies. Additionally, the average mean concentration field is found to scale with the IBL depth and the bulk velocity in the IBL., Fluid Mechanics, Atmospheric Physics, Atmospheric Remote Sensing

Simultaneous particle-image velocimetry and laser-induced fluorescence combined with large-eddy simulations are used to investigate the flow and pollutant dispersion behaviour in a rural-to-urban roughness transition. The urban roughness is characterized by an array of cubical obstacles in an aligned arrangement. A plane fence is added one obstacle height h upstream of the urban roughness elements, with three different fence heights considered. A smooth-wall turbulent boundary layer with a depth of 10h is used as the approaching flow, and a passive tracer is released from a uniform line source 1h upstream of the fence. A shear layer is formed at the top of the fence, which increases in strength for the higher fence cases, resulting in a deeper internal boundary layer (IBL). It is found that the mean flow for the rural-to-urban transition can be described by means of a mixing-length model provided that the transitional effects are accounted for. The mixing-length formulation for sparse urban canopies, as found in the literature, is extended to take into account the blockage effect in dense canopies. Additionally, the average mean concentration field is found to scale with the IBL depth and the bulk velocity in the IBL., Fluid Mechanics, Atmospheric Physics, Atmospheric Remote Sensing

Both large-eddy simulations (LES) and water-tunnel experiments, using simultaneous stereoscopic particle image velocimetry and laser-induced fluorescence, have been used to investigate pollutant dispersion mechanisms in regions where the surface changes from rural to urban roughness. The urban roughness was characterized by an array of rectangular obstacles in an in-line arrangement. The streamwise length scale of the roughness was kept constant, while the spanwise length scale was varied by varying the obstacle aspect ratio l / h between 1 and 8, where l is the spanwise dimension of the obstacles and h is the height of the obstacles. Additionally, the case of two-dimensional roughness (riblets) was considered in LES. A smooth-wall turbulent boundary layer of depth 10h was used as the approaching flow, and a line source of passive tracer was placed 2h upstream of the urban canopy. The experimental and numerical results show good agreement, while minor discrepancies are readily explained. It is found that for (Formula presented.) the drag induced by the urban canopy is largest of all considered cases, and is caused by a large-scale secondary flow. In addition, due to the roughness transition the vertical advective pollutant flux is the main ventilation mechanism in the first three streets. Furthermore, by means of linear stochastic estimation the mean flow structure is identified that is responsible for street-canyon ventilation for the sixth street and onwards. Moreover, it is shown that the vertical length scale of this structure increases with increasing aspect ratio of the obstacles in the canopy, while the streamwise length scale does not show a similar trend., Fluid Mechanics, Atmospheric Physics, Atmospheric Remote Sensing

Both large-eddy simulations (LES) and water-tunnel experiments, using simultaneous stereoscopic particle image velocimetry and laser-induced fluorescence, have been used to investigate pollutant dispersion mechanisms in regions where the surface changes from rural to urban roughness. The urban roughness was characterized by an array of rectangular obstacles in an in-line arrangement. The streamwise length scale of the roughness was kept constant, while the spanwise length scale was varied by varying the obstacle aspect ratio l / h between 1 and 8, where l is the spanwise dimension of the obstacles and h is the height of the obstacles. Additionally, the case of two-dimensional roughness (riblets) was considered in LES. A smooth-wall turbulent boundary layer of depth 10h was used as the approaching flow, and a line source of passive tracer was placed 2h upstream of the urban canopy. The experimental and numerical results show good agreement, while minor discrepancies are readily explained. It is found that for (Formula presented.) the drag induced by the urban canopy is largest of all considered cases, and is caused by a large-scale secondary flow. In addition, due to the roughness transition the vertical advective pollutant flux is the main ventilation mechanism in the first three streets. Furthermore, by means of linear stochastic estimation the mean flow structure is identified that is responsible for street-canyon ventilation for the sixth street and onwards. Moreover, it is shown that the vertical length scale of this structure increases with increasing aspect ratio of the obstacles in the canopy, while the streamwise length scale does not show a similar trend., Fluid Mechanics, Atmospheric Physics, Atmospheric Remote Sensing

Large-eddy simulations (LES) are used to investigate the effect of stable stratification on rural-to-urban roughness transitions. Smooth-wall turbulent boundary layers are subjected to a generic urban roughness consisting of cubes in an in-line arrangement. Two line sources of pollutant are added to investigate the effect on pollutant dispersion. Firstly, the LES method is validated with data from wind-tunnel experiments on fully-developed flow over cubical roughness. Good agreement is found for the vertical profiles of the mean streamwise velocity component and mean Reynolds stress. Subsequently, roughness transition simulations are done for both neutral and stable conditions. Results are compared with fully-developed simulations with conventional double-periodic boundary conditions. In stable conditions, at the end of the domain the streamwise velocity component has not yet reached the fully-developed state even though the surface forces are nearly constant. Moreover, the internal boundary layer is shallower than in the neutral case. Furthermore, an investigation of the turbulence kinetic energy budget shows that the buoyancy destruction term is reduced in the internal boundary layer, above which it is equal to the undisturbed (smooth wall) value. In addition, in stable conditions pollutants emitted above the urban canopy enter the canopy farther downstream due to decreased vertical mixing. Pollutants emitted below the top of the urban canopy are 85 % higher in concentration in stable conditions mostly due to decreased advection. If this is taken into account concentrations remain 17 % greater in stable conditions due to less rapid internal boundary-layer growth. Finally, it is concluded that in the first seven streets the vertical advective pollutant flux is significant, in contrast to the fully-developed case., Process and Energy, Mechanical, Maritime and Materials Engineering

Conditional Markov chain (CMC) models have proven to be promising building blocks for stochastic convection parameterizations. In this paper, it is demonstrated how two different CMC models can be used as mass flux closures in convection parameterizations. More specifically, the CMC models provide a stochastic estimate of the convective area fraction that is directly proportional to the cloud-base mass flux. Since, in one of the models, the number of CMCs decreases with increasing resolution, this approach makes convection parameterizations scale aware and introduces stochastic fluctuations that increase with resolution in a realistic way. Both CMC models are implemented in a GCM of intermediate complexity. It is shown that with the CMC models, trained with observational data, it is possible to improve both the subgrid-scale variability and the autocorrelation function of the cloud-base mass flux as well as the distribution of the daily accumulated precipitation in the tropics. Hovmöller diagrams and wavenumber–frequency diagrams of the equatorial precipitation indicate that, in this specific GCM, convectively coupled equatorial waves are more sensitive to the mean cloud-base mass flux than to stochastic fluctuations. A smaller mean mass flux tends to increase the power of the simulated MJO and to diminish equatorial Kelvin waves., Geoscience and Remote Sensing, Civil Engineering and Geosciences

Geoscience and Remote Sensing, Civil Engineering and Geosciences

The low-frequency contribution to the systematic and random sampling errors in single-tower eddy-covariance flux measurements is investigated using large-eddy simulation (LES). We use a continuous LES integration that covers a full year of realistic weather conditions over Cabauw, the Netherlands, and emulate eddy-covariance measurements. We focus on the daytime flux imbalance, when the turbulent flux is sufficiently resolved. Averaged over the year, daytime single-tower eddy-covariance flux measurements lead to a significant systematic underestimation of the turbulent flux. This underestimation depends on the averaging period and measurement height. For a 3600-s averaging period at 16-m height, the systematic underestimation reduces to a few percent, but for 900-s averaged tall-tower measurements at 100-m height, the fluxes are systematically underestimated by over 20 %. The year-long dataset facilitates an investigation into the environmental conditions that influence the eddy-covariance flux imbalance. The imbalance problem is found to vary widely from day to day, strongly dependent on the flow regime. In general, the imbalance problem reduces with increased mean wind speed, but days having the largest imbalance (over twice the average) are characterized by roll vortices that occur for average wind speeds, typically having a boundary-layer height (zi) to Obukhov length (L) ratio of 10

Large-eddy simulations (LES) are used to investigate the effect of stable stratification on rural-to-urban roughness transitions. Smooth-wall turbulent boundary layers are subjected to a generic urban roughness consisting of cubes in an in-line arrangement. Two line sources of pollutant are added to investigate the effect on pollutant dispersion. Firstly, the LES method is validated with data from wind-tunnel experiments on fully-developed flow over cubical roughness. Good agreement is found for the vertical profiles of the mean streamwise velocity component and mean Reynolds stress. Subsequently, roughness transition simulations are done for both neutral and stable conditions. Results are compared with fully-developed simulations with conventional double-periodic boundary conditions. In stable conditions, at the end of the domain the streamwise velocity component has not yet reached the fully-developed state even though the surface forces are nearly constant. Moreover, the internal boundary layer is shallower than in the neutral case. Furthermore, an investigation of the turbulence kinetic energy budget shows that the buoyancy destruction term is reduced in the internal boundary layer, above which it is equal to the undisturbed (smooth wall) value. In addition, in stable conditions pollutants emitted above the urban canopy enter the canopy farther downstream due to decreased vertical mixing. Pollutants emitted below the top of the urban canopy are 85 % higher in concentration in stable conditions mostly due to decreased advection. If this is taken into account concentrations remain 17 % greater in stable conditions due to less rapid internal boundary-layer growth. Finally, it is concluded that in the first seven streets the vertical advective pollutant flux is significant, in contrast to the fully-developed case., Process and Energy, Mechanical, Maritime and Materials Engineering

Conditional Markov chain (CMC) models have proven to be promising building blocks for stochastic convection parameterizations. In this paper, it is demonstrated how two different CMC models can be used as mass flux closures in convection parameterizations. More specifically, the CMC models provide a stochastic estimate of the convective area fraction that is directly proportional to the cloud-base mass flux. Since, in one of the models, the number of CMCs decreases with increasing resolution, this approach makes convection parameterizations scale aware and introduces stochastic fluctuations that increase with resolution in a realistic way. Both CMC models are implemented in a GCM of intermediate complexity. It is shown that with the CMC models, trained with observational data, it is possible to improve both the subgrid-scale variability and the autocorrelation function of the cloud-base mass flux as well as the distribution of the daily accumulated precipitation in the tropics. Hovmöller diagrams and wavenumber–frequency diagrams of the equatorial precipitation indicate that, in this specific GCM, convectively coupled equatorial waves are more sensitive to the mean cloud-base mass flux than to stochastic fluctuations. A smaller mean mass flux tends to increase the power of the simulated MJO and to diminish equatorial Kelvin waves., Geoscience and Remote Sensing, Civil Engineering and Geosciences

Geoscience and Remote Sensing, Civil Engineering and Geosciences

The low-frequency contribution to the systematic and random sampling errors in single-tower eddy-covariance flux measurements is investigated using large-eddy simulation (LES). We use a continuous LES integration that covers a full year of realistic weather conditions over Cabauw, the Netherlands, and emulate eddy-covariance measurements. We focus on the daytime flux imbalance, when the turbulent flux is sufficiently resolved. Averaged over the year, daytime single-tower eddy-covariance flux measurements lead to a significant systematic underestimation of the turbulent flux. This underestimation depends on the averaging period and measurement height. For a 3600-s averaging period at 16-m height, the systematic underestimation reduces to a few percent, but for 900-s averaged tall-tower measurements at 100-m height, the fluxes are systematically underestimated by over 20 %. The year-long dataset facilitates an investigation into the environmental conditions that influence the eddy-covariance flux imbalance. The imbalance problem is found to vary widely from day to day, strongly dependent on the flow regime. In general, the imbalance problem reduces with increased mean wind speed, but days having the largest imbalance (over twice the average) are characterized by roll vortices that occur for average wind speeds, typically having a boundary-layer height (zi) to Obukhov length (L) ratio of 10

Results are presented of two large-eddy simulation (LES) runs of the entire year 2012 centered at the Cabauw observational supersite in the Netherlands. The LES is coupled to a regional weather model that provides the large-scale information. The simulations provide three-dimensional continuous time series of LES-generated turbulence and clouds, which can be compared in detail to the extensive observational dataset of Cabauw. The LES dataset is available from the authors on request. This type of LES setup has a number of advantages. First, it can provide a more statistical approach to the study of turbulent atmospheric flow than the more common case studies, since a diverse but representative set of conditions is covered, including numerous transitions. This has advantages in the design and evaluation of parameterizations. Second, the setup can provide valuable information on the quality of the LES model when applied to such a wide range of conditions. Last, it also provides the possibility to emulate observation techniques. This might help detect limitations and potential problems of a variety of measurement techniques. The LES runs are validated through a comparison with observations from the observational supersite and with results from the ‘‘parent’’ large-scale model. The long time series that are generated, in combination with information on the spatial structure, provide a novel opportunity to study time scales ranging from seconds to seasons. This facilitates a study of the power spectrum of horizontal and vertical wind speed variance to identify the dominant variance-containing time scales., Geoscience and Remote Sensing, Civil Engineering and Geosciences

Predicting pollutant dispersion in urban environments requires accurate treatment of obstacle geometry, inflow turbulence and temperature differences. This paper considers both the influence of thermal stratification and the presence of a single obstacle on pollutant dispersion in turbulent boundary layers (TBLs). Turbulent flow over a fence with line sources of pollutant in its vicinity is simulated by means of Large-Eddy Simulations. Separate ‘driver’ simulations are done to generate the inflow TBL for several levels of stratification. Using these inflow TBLs the flow development and pollutant dispersion behind the fence, up to 100 fence heights, h, is investigated. It is shown that the decay of velocity and temperature deficit is independent of stability, while the decay of Reynolds stress and concentration excess decreases with increasing stability. For neutral cases the influence of the obstacle is gone after approximately 75h, while for stable cases near the ground the flow is still accelerated compared to the undisturbed case. The fence does cause a local reduction of stratification and thereby increased pollutant dispersion. However, neglecting the effect of buoyancy results in an underestimation of pollutant concentration by a factor 2.5 at 75h downstream of the emission source for the most stable case., Process and Energy, Mechanical, Maritime and Materials Engineering

The distribution of relative velocities between particles provides invaluable information on the rates and characteristics of particle collisions. We show that the theoretical model of Gustavsson and Mehlig [K. Gustavsson and B. Mehlig, J. Turbul. 15, 34 (2014)], within its anticipated limits of validity, can predict the joint probability density function of relative velocities and separations of identical inertial particles in isotropic turbulent flows with remarkable accuracy. We also quantify the validity range of the model. The model matches two limits (or two types) of relative motion between particles: one where pair diffusion dominates (i.e., large coherence between particle motion) and one where caustics dominate (i.e., large velocity differences between particles at small separations). By using direct numerical simulation combined with Lagrangian particle tracking, we assess the model prediction in homogeneous and isotropic turbulence. We demonstrate that, when sufficient caustics are present at a given separation and the particle response time is significantly smaller than the integral time scales of the flow, the distribution exhibits the same universal power-law form dictated by the correlation dimension as predicted by the model of Gustavsson and Mehlig. In agreement with the model, no strong dependency on the Taylor-based Reynolds number is observed., Geoscience & Remote Sensing, Civil Engineering and Geosciences

Since the advent of computers midway through the twentieth century, computational resources have increased exponentially. It is likely they will continue to do so, especially when accounting for recent trends in multicore processors. History has shown that such an increase tends to directly lead to weather and climate models that readily exploit the extra resources, improving model quality and resolution. We show that Large-Eddy Simulation (LES) models that utilize modern, accelerated (e.g., by GPU or coprocessor), parallel hardware systems can now provide turbulence-resolving numerical weather forecasts over a region the size of the Netherlands at 100-m resolution. This approach has the potential to speed the development of turbulence-resolving numerical weather prediction models., Geoscience and Remote Sensing, Civil Engineering and Geosciences

Results are presented of two large-eddy simulation (LES) runs of the entire year 2012 centered at the Cabauw observational supersite in the Netherlands. The LES is coupled to a regional weather model that provides the large-scale information. The simulations provide three-dimensional continuous time series of LES-generated turbulence and clouds, which can be compared in detail to the extensive observational dataset of Cabauw. The LES dataset is available from the authors on request. This type of LES setup has a number of advantages. First, it can provide a more statistical approach to the study of turbulent atmospheric flow than the more common case studies, since a diverse but representative set of conditions is covered, including numerous transitions. This has advantages in the design and evaluation of parameterizations. Second, the setup can provide valuable information on the quality of the LES model when applied to such a wide range of conditions. Last, it also provides the possibility to emulate observation techniques. This might help detect limitations and potential problems of a variety of measurement techniques. The LES runs are validated through a comparison with observations from the observational supersite and with results from the ‘‘parent’’ large-scale model. The long time series that are generated, in combination with information on the spatial structure, provide a novel opportunity to study time scales ranging from seconds to seasons. This facilitates a study of the power spectrum of horizontal and vertical wind speed variance to identify the dominant variance-containing time scales., Geoscience and Remote Sensing, Civil Engineering and Geosciences

Predicting pollutant dispersion in urban environments requires accurate treatment of obstacle geometry, inflow turbulence and temperature differences. This paper considers both the influence of thermal stratification and the presence of a single obstacle on pollutant dispersion in turbulent boundary layers (TBLs). Turbulent flow over a fence with line sources of pollutant in its vicinity is simulated by means of Large-Eddy Simulations. Separate ‘driver’ simulations are done to generate the inflow TBL for several levels of stratification. Using these inflow TBLs the flow development and pollutant dispersion behind the fence, up to 100 fence heights, h, is investigated. It is shown that the decay of velocity and temperature deficit is independent of stability, while the decay of Reynolds stress and concentration excess decreases with increasing stability. For neutral cases the influence of the obstacle is gone after approximately 75h, while for stable cases near the ground the flow is still accelerated compared to the undisturbed case. The fence does cause a local reduction of stratification and thereby increased pollutant dispersion. However, neglecting the effect of buoyancy results in an underestimation of pollutant concentration by a factor 2.5 at 75h downstream of the emission source for the most stable case., Process and Energy, Mechanical, Maritime and Materials Engineering

The distribution of relative velocities between particles provides invaluable information on the rates and characteristics of particle collisions. We show that the theoretical model of Gustavsson and Mehlig [K. Gustavsson and B. Mehlig, J. Turbul. 15, 34 (2014)], within its anticipated limits of validity, can predict the joint probability density function of relative velocities and separations of identical inertial particles in isotropic turbulent flows with remarkable accuracy. We also quantify the validity range of the model. The model matches two limits (or two types) of relative motion between particles: one where pair diffusion dominates (i.e., large coherence between particle motion) and one where caustics dominate (i.e., large velocity differences between particles at small separations). By using direct numerical simulation combined with Lagrangian particle tracking, we assess the model prediction in homogeneous and isotropic turbulence. We demonstrate that, when sufficient caustics are present at a given separation and the particle response time is significantly smaller than the integral time scales of the flow, the distribution exhibits the same universal power-law form dictated by the correlation dimension as predicted by the model of Gustavsson and Mehlig. In agreement with the model, no strong dependency on the Taylor-based Reynolds number is observed., Geoscience & Remote Sensing, Civil Engineering and Geosciences

Since the advent of computers midway through the twentieth century, computational resources have increased exponentially. It is likely they will continue to do so, especially when accounting for recent trends in multicore processors. History has shown that such an increase tends to directly lead to weather and climate models that readily exploit the extra resources, improving model quality and resolution. We show that Large-Eddy Simulation (LES) models that utilize modern, accelerated (e.g., by GPU or coprocessor), parallel hardware systems can now provide turbulence-resolving numerical weather forecasts over a region the size of the Netherlands at 100-m resolution. This approach has the potential to speed the development of turbulence-resolving numerical weather prediction models., Geoscience and Remote Sensing, Civil Engineering and Geosciences

This study investigates the droplet dynamics at the lateral cloud–environment interface in shallow cumulus clouds. A mixing layer is used to study a small part of the cloud edge using direct numerical simulation combined with a Lagrangian particle tracking and collision algorithm. The effect of evaporation, gravity, coalescence, and the initial droplet size distribution on the intensity of the mixing layer and the evolution of the droplet size distribution is studied. Mixing of the droplets with environmental air induces evaporative cooling, which results in a very characteristic subsiding shell. As a consequence, stronger horizontal velocity gradients are found in the mixing layer, which induces more mixing and evaporation. A broadening of the droplet size distribution is observed as a result of evaporation and coalescence. Gravity acting on the droplets allows droplets in cloudy filaments detrained from the cloud to sediment and remain longer in the unsaturated environment. While this effect of gravity did not have a significant impact in this case on the mean evolution of the mixing layer, it does contribute to the broadening of the droplet size distribution and thereby significantly increases the collision rate. Although more but smaller droplets result in more evaporative cooling, more droplets also increase small-scale fluctuations and the production of turbulent dissipation. For the smallest droplets considered with a radius of 10 mm, the authors found that, although a more pronounced buoyancy dip was present, the increase in dissipation rate actually led to a decrease in the turbulent intensity of the mixing layer. Extrapolation of the results to realistic clouds is discussed., Geoscience and Remote Sensing, Civil Engineering and Geosciences

This study investigates the local flow characteristics near droplet-droplet collisions by means of direct numerical simulation of isotropic cloudlike turbulence. The key finding is that, generally, droplets do not collide where they preferentially concentrate. Preferential concentration is found to happen as expected in regions of low enstrophy (vorticity magnitude), but collisions tend to take place in regions with significantly higher dissipation rates (up to a factor of 2.5 for Stokes unity droplets). Investigation of the droplet history reveals that collisions are consistently preceded by dissipative events. Based on the droplet history data, the following physical picture of a collision can be constructed: Enstrophy makes droplets preferentially concentrate in quiescent flow regions, thereby increasing the droplet velocity coherence, i.e., decreasing relative velocities between droplets. Strongly clustered droplets thus have a low collision probability, until a dissipative event accelerates the droplets towards each other. We study the relation between the local dissipation rate and the local collision kernel and vary the averaging scale to relate the results to the globally averaged collision and dissipation rates. It is noted that, unlike enstrophy, there is a positive correlation between the dissipation rate and collision efficiency that extends from the largest to the smallest scales of the flow., Geoscience & Remote Sensing, Civil Engineering and Geosciences

A mixed-layer model is used to study the response of stratocumulus equilibrium state solutions to perturbations of cloud controlling factors which include the sea surface temperature, the specific humidity and temperature in the free troposphere, as well as the large-scale divergence and horizontal wind speed. In the first set of experiments, we assess the effect of a change in a single forcing condition while keeping the entrainment rate fixed, while in the second set, the entrainment rate is allowed to respond. The role of the entrainment rate is exemplified from an experiment in which the sea surface temperature is increased. An analysis of the budget equation for heat and moisture demonstrates that for a fixed entrainment rate, the stratocumulus liquid water path (LWP) will increase since the moistening from the surface evaporation dominates the warming effect. By contrast, if the response of the entrainment rate to the change in the surface forcing is sufficiently strong, enhanced mixing of dry and warm inversion air will cause a thinning of the cloud layer. If the entrainment warming effect is sufficiently strong, the surface sensible heat flux will decrease, as opposed to an increase which will occur for a fixed entrainment rate. It is argued that the surface evaporation will always increase for an increase in the sea surface temperature, and this change will be enlarged if the entrainment rate increases. These experiments aid the interpretation of results of similar simulations with single-column model versions of climate models carried out in the framework of the CFMIP-GCSS Intercomparison of Large-Eddy and Single-Column Models (CGILS) project. Because in a large-scale models, the entrainment response to changes in the large-scale forcing conditions depends on the details of the parameterization of turbulent and convective transport, intermodel differences in the sign of the LWP response may be well attributable to differences in the entrainment response., Geoscience & Remote Sensing, Civil Engineering and Geosciences

Mixing processes in deep precipitating cumulus clouds are investigated by tracking Lagrangian particles in a large-eddy simulation. The trajectories of particles are reconstructed and the thermodynamic properties of cloud air are studied using mixing diagrams. The trajectory analysis shows that the in-cloud mixing is entirely dominated by lateral entrainment and that there is no significant vertical mixing by downdrafts originating from cloud top. Yet the thermodynamic properties of the particles are located close to a line in the mixing diagrams, which appears to be consistent with two-point vertical mixing. An attempt is made to resolve this paradox using the buoyancy-sorting model of Taylor and Baker, but it is found that this model does not provide a full explanation for the location of particles in the mixing diagram. However, it is shown that the mixing-line behavior can be well understood from a simple analytically solvable model that uses a range of different lateral entrainment rates. Two further factors that determine the location of particles in the mixing diagram are identified: the removal of noncloudy air and precipitation effects. Finally, a thermodynamic argument is given that explains the absence of coherent downdrafts descending from cloud top., Geoscience & Remote Sensing, Civil Engineering and Geosciences

Mixing processes in deep precipitating cumulus clouds are investigated by tracking Lagrangian particles in a large-eddy simulation. The trajectories of particles are reconstructed and the thermodynamic properties of cloud air are studied using mixing diagrams. The trajectory analysis shows that the in-cloud mixing is entirely dominated by lateral entrainment and that there is no significant vertical mixing by downdrafts originating from cloud top. Yet the thermodynamic properties of the particles are located close to a line in the mixing diagrams, which appears to be consistent with two-point vertical mixing. An attempt is made to resolve this paradox using the buoyancy-sorting model of Taylor and Baker, but it is found that this model does not provide a full explanation for the location of particles in the mixing diagram. However, it is shown that the mixing-line behavior can be well understood from a simple analytically solvable model that uses a range of different lateral entrainment rates. Two further factors that determine the location of particles in the mixing diagram are identified: the removal of noncloudy air and precipitation effects. Finally, a thermodynamic argument is given that explains the absence of coherent downdrafts descending from cloud top., Geoscience & Remote Sensing, Civil Engineering and Geosciences

A mixed-layer model is used to study the response of stratocumulus equilibrium state solutions to perturbations of cloud controlling factors which include the sea surface temperature, the specific humidity and temperature in the free troposphere, as well as the large-scale divergence and horizontal wind speed. In the first set of experiments, we assess the effect of a change in a single forcing condition while keeping the entrainment rate fixed, while in the second set, the entrainment rate is allowed to respond. The role of the entrainment rate is exemplified from an experiment in which the sea surface temperature is increased. An analysis of the budget equation for heat and moisture demonstrates that for a fixed entrainment rate, the stratocumulus liquid water path (LWP) will increase since the moistening from the surface evaporation dominates the warming effect. By contrast, if the response of the entrainment rate to the change in the surface forcing is sufficiently strong, enhanced mixing of dry and warm inversion air will cause a thinning of the cloud layer. If the entrainment warming effect is sufficiently strong, the surface sensible heat flux will decrease, as opposed to an increase which will occur for a fixed entrainment rate. It is argued that the surface evaporation will always increase for an increase in the sea surface temperature, and this change will be enlarged if the entrainment rate increases. These experiments aid the interpretation of results of similar simulations with single-column model versions of climate models carried out in the framework of the CFMIP-GCSS Intercomparison of Large-Eddy and Single-Column Models (CGILS) project. Because in a large-scale models, the entrainment response to changes in the large-scale forcing conditions depends on the details of the parameterization of turbulent and convective transport, intermodel differences in the sign of the LWP response may be well attributable to differences in the entrainment response., Geoscience & Remote Sensing, Civil Engineering and Geosciences

This study investigates the local flow characteristics near droplet-droplet collisions by means of direct numerical simulation of isotropic cloudlike turbulence. The key finding is that, generally, droplets do not collide where they preferentially concentrate. Preferential concentration is found to happen as expected in regions of low enstrophy (vorticity magnitude), but collisions tend to take place in regions with significantly higher dissipation rates (up to a factor of 2.5 for Stokes unity droplets). Investigation of the droplet history reveals that collisions are consistently preceded by dissipative events. Based on the droplet history data, the following physical picture of a collision can be constructed: Enstrophy makes droplets preferentially concentrate in quiescent flow regions, thereby increasing the droplet velocity coherence, i.e., decreasing relative velocities between droplets. Strongly clustered droplets thus have a low collision probability, until a dissipative event accelerates the droplets towards each other. We study the relation between the local dissipation rate and the local collision kernel and vary the averaging scale to relate the results to the globally averaged collision and dissipation rates. It is noted that, unlike enstrophy, there is a positive correlation between the dissipation rate and collision efficiency that extends from the largest to the smallest scales of the flow., Geoscience & Remote Sensing, Civil Engineering and Geosciences

Geoscience and Remote Sensing, Civil Engineering and Geosciences

A modeling framework is developed that extends the mixed-layer model to steady-state cumulus convection. The aim is to consider the simplest model that retains the essential behavior of cumulus-capped layers. The presented framework allows for the evaluation of stationary states dependent on external parameters. These states are completely independent of the initial conditions, and therefore represent an asymptote that might help deepen understanding of the dependence of the cloudy boundary layer on external forcings. Formulating separate equations for the lifting condensation level and the mixed-layer height, the dry and wet energetics can be distinguished. Regimes that can support steady-state cumulus clouds and regimes that cannot are identified by comparison of the dry and wet buoyancy effects. The dominant mechanisms that govern the creation and eventual depth of the cloud layer are identified. Model predictions are tested by comparison with a large number of independent large-eddy simulations for varying surface and large-scale conditions and are found to be in good agreement., Geoscience and Remote Sensing, Civil Engineering and Geosciences

A modeling framework is developed that extends the mixed-layer model to steady-state cumulus convection. The aim is to consider the simplest model that retains the essential behavior of cumulus-capped layers. The presented framework allows for the evaluation of stationary states dependent on external parameters. These states are completely independent of the initial conditions, and therefore represent an asymptote that might help deepen understanding of the dependence of the cloudy boundary layer on external forcings. Formulating separate equations for the lifting condensation level and the mixed-layer height, the dry and wet energetics can be distinguished. Regimes that can support steady-state cumulus clouds and regimes that cannot are identified by comparison of the dry and wet buoyancy effects. The dominant mechanisms that govern the creation and eventual depth of the cloud layer are identified. Model predictions are tested by comparison with a large number of independent large-eddy simulations for varying surface and large-scale conditions and are found to be in good agreement., Geoscience and Remote Sensing, Civil Engineering and Geosciences

Geoscience and Remote Sensing, Civil Engineering and Geosciences

The collapse of turbulence in the nocturnal boundary layer is studied by means of a simple bulk model that describes the basic physical interactions in the surface energy balance. It is shown that for a given mechanical forcing, the amount of turbulent heat that can be transported downward is limited to a certain maximum. In the case of weak winds and clear skies, this maximum can be significantly smaller than the net radiative loss minus soil heat transport. In the case when the surface has low heat capacity, this imbalance generates rapid surface cooling that further suppresses the turbulent heat transport, so that eventually turbulence largely ceases (positive feedback mechanism). The model predicts the minimum wind speed for sustainable turbulence for the so-called crossing level. At this level, some decameters above the surface, the wind is relatively stationary compared to lower and higher levels. The critical speed is predicted in the range of about 5–7 m s21, depending on radiative forcing and surface properties, and is in agreement with observations at Cabauw. The critical value appears not very sensitive to model details or to the exact values of the input parameters. Finally, results are interpreted in terms of external forcings, such as geostrophic wind. As it is generally larger than the speed at crossing height, a 5 m s21 geostrophic wind may be considered as the typical limit below which sustainable, continuous turbulence under clear-sky conditions is unlikely to exist. Below this threshold emergence of the very stable nocturnal boundary layer is anticipated., Multi-Scale Physics, Applied Sciences

The mechanism behind the collapse of turbulence in the evening as a precursor to the onset of the very stable boundary layer is investigated. To this end a cooled, pressure-driven flow is investigated by means of a local similarity model. Simulations reveal a temporary collapse of turbulence whenever the surface heat extraction, expressed in its nondimensional form h/L, exceeds a critical value. As any temporary reduction of turbulent friction is followed by flow acceleration, the long-term state is unconditionally turbulent. In contrast, the temporary cessation of turbulence, which may actually last for several hours in the nocturnal boundary layer, can be understood from the fact that the time scale for boundary layer diffusion is much smaller than the time scale for flow acceleration. This limits the available momentum that can be used for downward heat transport. In case the surface heat extraction exceeds the so-called maximum sustainable heat flux (MSHF), the near-surface inversion rapidly increases. Finally, turbulent activity is largely suppressed by the intense density stratification that supports the emergence of a different, calmer boundary layer regime., Multi-Scale Physics, Applied Sciences

The rapid transition from shallow to deep convection is investigated using large-eddy simulations. The role of cold pools, which occur due to the evaporation of rainfall, is explored using a series of experiments in which their formation is suppressed.A positive feedback occurs: the presence of cold pools promotes deeper, wider, and more buoyant clouds with higher precipitation rates, which in turn lead to stronger cold pools. To assess the influence of the subcloud layer on the development of deep convection, the coupling between the cloud layer and the subcloud layer is explored using Lagrangian particle trajectories. As shown in previous studies, particles that enter clouds have properties that deviate significantly from the mean state. However, the differences between particles that enter shallow and deep clouds are remarkably small in the subcloud layer, and become larger in the cloud layer, indicating different entrainment rates. The particles that enter the deepest clouds also correspond to the widest cloud bases, which points to the importance of convective organization within the subcloud layer., Geoscience and Remote Sensing, Civil Engineering and Geosciences

This study explores the mechanisms that determine detrainment in deep cumulus convection. A set of 90 high-resolution Large Eddy Simulations is used to systematically explore the sensitivity of continental deep convection to the relative humidity and stability of the free troposphere. It appears that variations in the mass-flux profiles are determined by detrainment, rather than entrainment. The detrainment shows a strong dependence on the critical mixing ratio, a dimensionless parameter which describes which mixtures of cloud core and environmental air are positively buoyant. A conceptual approach to the parameterization of detrainment is proposed on the basis of these results., Geoscience & Remote Sensing, Civil Engineering and Geosciences

Multi-Scale Physics, Applied Sciences

The mechanism behind the collapse of turbulence in the evening as a precursor to the onset of the very stable boundary layer is investigated. To this end a cooled, pressure-driven flow is investigated by means of a local similarity model. Simulations reveal a temporary collapse of turbulence whenever the surface heat extraction, expressed in its nondimensional form h/L, exceeds a critical value. As any temporary reduction of turbulent friction is followed by flow acceleration, the long-term state is unconditionally turbulent. In contrast, the temporary cessation of turbulence, which may actually last for several hours in the nocturnal boundary layer, can be understood from the fact that the time scale for boundary layer diffusion is much smaller than the time scale for flow acceleration. This limits the available momentum that can be used for downward heat transport. In case the surface heat extraction exceeds the so-called maximum sustainable heat flux (MSHF), the near-surface inversion rapidly increases. Finally, turbulent activity is largely suppressed by the intense density stratification that supports the emergence of a different, calmer boundary layer regime., Multi-Scale Physics, Applied Sciences

The rapid transition from shallow to deep convection is investigated using large-eddy simulations. The role of cold pools, which occur due to the evaporation of rainfall, is explored using a series of experiments in which their formation is suppressed.A positive feedback occurs: the presence of cold pools promotes deeper, wider, and more buoyant clouds with higher precipitation rates, which in turn lead to stronger cold pools. To assess the influence of the subcloud layer on the development of deep convection, the coupling between the cloud layer and the subcloud layer is explored using Lagrangian particle trajectories. As shown in previous studies, particles that enter clouds have properties that deviate significantly from the mean state. However, the differences between particles that enter shallow and deep clouds are remarkably small in the subcloud layer, and become larger in the cloud layer, indicating different entrainment rates. The particles that enter the deepest clouds also correspond to the widest cloud bases, which points to the importance of convective organization within the subcloud layer., Geoscience and Remote Sensing, Civil Engineering and Geosciences

This study explores the mechanisms that determine detrainment in deep cumulus convection. A set of 90 high-resolution Large Eddy Simulations is used to systematically explore the sensitivity of continental deep convection to the relative humidity and stability of the free troposphere. It appears that variations in the mass-flux profiles are determined by detrainment, rather than entrainment. The detrainment shows a strong dependence on the critical mixing ratio, a dimensionless parameter which describes which mixtures of cloud core and environmental air are positively buoyant. A conceptual approach to the parameterization of detrainment is proposed on the basis of these results., Geoscience & Remote Sensing, Civil Engineering and Geosciences

The collapse of turbulence in the nocturnal boundary layer is studied by means of a simple bulk model that describes the basic physical interactions in the surface energy balance. It is shown that for a given mechanical forcing, the amount of turbulent heat that can be transported downward is limited to a certain maximum. In the case of weak winds and clear skies, this maximum can be significantly smaller than the net radiative loss minus soil heat transport. In the case when the surface has low heat capacity, this imbalance generates rapid surface cooling that further suppresses the turbulent heat transport, so that eventually turbulence largely ceases (positive feedback mechanism). The model predicts the minimum wind speed for sustainable turbulence for the so-called crossing level. At this level, some decameters above the surface, the wind is relatively stationary compared to lower and higher levels. The critical speed is predicted in the range of about 5–7 m s21, depending on radiative forcing and surface properties, and is in agreement with observations at Cabauw. The critical value appears not very sensitive to model details or to the exact values of the input parameters. Finally, results are interpreted in terms of external forcings, such as geostrophic wind. As it is generally larger than the speed at crossing height, a 5 m s21 geostrophic wind may be considered as the typical limit below which sustainable, continuous turbulence under clear-sky conditions is unlikely to exist. Below this threshold emergence of the very stable nocturnal boundary layer is anticipated., Multi-Scale Physics, Applied Sciences

Multi-Scale Physics, Applied Sciences