High-resolution Large-eddy Simulation Research Articles

The dynamics of concentration fluctuations within passive scalar plumes in a turbulent neutral boundary layer

We investigate the concentration fluctuations of passive scalar plumes emitted from small, localised (point-like) steady sources in a neutrally stratified turbulent boundary layer over a rough wall. The study utilises high-resolution large-eddy simulations for sources of varying sizes and heights. The numerical results, which show good agreement with wind-tunnel studies, are used to estimate statistical indicators of the concentration field, including spectra and moments up to the fourth order. These allow us to elucidate the mechanisms responsible for the production, transport and dissipation of concentration fluctuations, with a focus on the very near field, where the skewness is found to have negative values – an aspect not previously highlighted. The gamma probability density function is confirmed to be a robust model for the one-point concentration at sufficiently large distances from the source. However, for ground-level releases in a well-defined area around the plume centreline, the Gaussian distribution is found to be a better statistical model. As recently demonstrated by laboratory results, for elevated releases, the peak and shape of the pre-multiplied scalar spectra are confirmed to be independent of the crosswind location for a given downwind distance. Using a stochastic model and theoretical arguments, we demonstrate that this is due to the concentration spectra being directly shaped by the transverse and vertical velocity components governing the meandering of the plume. Finally, we investigate the intermittency factor, i.e. the probability of non-zero concentration, and analyse its variability depending on the thresholds adopted for its definition.

Aerosol composition, air quality, and boundary layer dynamics in the urban background of Stuttgart in winter

Abstract. Aerosol distributions are of great relevance for air quality, especially for cities like Stuttgart, which has limited air exchange due to its location in a basin. We collected a comprehensive set of data from remote sensing and in situ methods including radiosondes for the urban background of downtown Stuttgart to determine the impact of boundary layer mixing processes on local air quality and to evaluate the simulation results of the high-resolution large eddy simulation (LES) model PALM-4U at 10 m grid spacing. Stagnant meteorological conditions caused accumulation of aerosols, and chemical composition analysis shows that ammonium nitrate (37 ± 9 %) and organic aerosol (OA; 34 ± 9 %) dominated during this winter study. Case studies show that clouds during previous nights can weaken temperature inversion and accelerate boundary layer mixing after sunrise by up to 3 h. This is important for ground-level aerosol dilution during the morning rush hour. Furthermore, our observations validate results of the LES model PALM-4U in terms of boundary layer heights and aerosol mixing for 48 h. The simulated aerosol concentrations follow the trend of our observations but are still underestimated by a factor of 4.5 ± 2.1 due to missing secondary aerosol formation processes and uncertainties of emissions and boundary conditions in the model. This paper firstly evaluates the PALM-4U model performance in simulating aerosol spatio-temporal distributions, which can help to improve the LES model and to better understand sources and sinks for air pollution as well as the role of horizontal and vertical transport.

Implications of energy balance non-closure on carbon dioxide flux uncertainties: Insights from large eddy simulations in convective boundary layers

The non-closure of surface energy balance, often encountered in eddy covariance (EC) measurements, raises a critical query: does this non-closure lead to underestimated scalar fluxes, particularly CO2 flux (Fc), when using the same theoretical framework in EC? To address this question, we utilize high-resolution large-eddy simulations (LESs) to explore correlations between energy flux imbalances and Fc imbalances in convective boundary layers, considering both homogeneous and idealized heterogeneous surfaces. Our findings reveal that the unsteady CO2 or storage represents a leading factor influencing Fc imbalance, especially notable when the entrainment ratio for Fc is large. Even in scenarios with uniform surface Fcs, heterogeneous thermally-generated turbulence resulting from variable surface sensible heat flux (H) can induce substantial horizontal flux divergence, magnifying Fc imbalance. While a linear correlation between the energy flux imbalance and Fc imbalance arises under shared causative mechanisms (e.g., storage), complex correlations emerge if their influencing factors differ, contingent upon surface heterogeneity and site location. This complexity underscores the limitations in applying the closing methods for energy flux imbalance to the Fc imbalance.

Investigation of turbulence and interfacial exchange features of the gap area within the fully developed Shallow-Submerged canopy flow

The flow patterns within a longitudinal gap area formed by discontinuous distributions of submerged canopy, as well as the momentum and mass exchange characteristics between the gap area and the overlying free-flow, were studied using high-resolution Large Eddy Simulation (LES). The gap area is located within the fully developed region of submerged canopy flow. The simulations considered four aspect ratios of the gap area, L/h (ranging from 1 to 4), where L and h represent the span of the gap area and the height of the canopy, respectively, and two canopy densities, ϕ = 0.08 and 0.15. Results indicate that recirculation vortices appear only at ϕ = 0.15 and penetrate the downstream canopy patches to varying extents, with the distance of invasion decreasing as L/h increases. Influenced by the recirculation vortices, the bed shear stress in the downstream part of the gap area and the initial section of the downstream canopy patch is significantly increased compared to the fully developed region of the upstream canopy patch. Within the parameter range covered, vertical penetration of the mixing layer into the gap area always occurs, consistently falling into the shear layer growth regime, with significant enhancement of turbulence within the gap area even at L/h = 1. The high momentum entrainment elevates longitudinal velocity and turbulence intensity in the upper corner regions of the downstream canopy patch’s leading edge, combined with localized increases in bed shear stress, potentially destabilizing plants at the forefront of the downstream canopy patch. Although the total momentum exchange across the interface between the gap area and the upper free-flow layer is approximately independent of L/h, larger canopy densities lead to stronger momentum transport, and turbulent transport always dominates. Mass exchange generally increases with L/h, with more efficient vertical mass exchange in ϕ = 0.15 cases at L/h = 3 and 4.

Barriers and variable spacing enhance convective cooling and increase power output in solar PV plants

When the temperature of solar photovoltaic (PV) modules rises, efficiency drops and module degradation accelerates. Thus, it is beneficial to reduce module operating temperatures. Previous studies of solar power plants have illustrated that incoming flow characteristics, turbulent mixing, and array geometry can strongly impact convective cooling, as measured by the convective heat transfer coefficient h. In the fields of heat transfer and plant canopy flow, previous work has shown that system-scale arrangement modifications—e.g., variable spacing, barriers, or windbreaks—can passively alter the flow, enhance turbulent mixing, and influence convection. However, researchers have not yet explored how variable spacing or barriers might enhance convective cooling in solar power plants. Here, high-resolution large-eddy simulations model the air flow and heat transfer through solar power plant arrangements modified with missing modules and barrier walls. We then perform a control volume analysis to evaluate the net heat flux and compute h, which quantifies the influence of these spatial modifications on convective cooling and, thus, module temperature and power output. Installing barrier walls yields the greatest improvements, increasing h by 3.4%, reducing module temperature by an estimated 2.5 °C, and boosting power output by an estimated 1.4% on average. These findings indicate that incorporating variable spacing or barrier-type elements into PV plant designs can reduce module temperature and, thus, improve PV performance and service life.

Effects of inflow velocity on transverse jet injection in a supersonic cavity combustor

The flow, mixing, and combustion mechanisms in the wide range scramjet engine are complex and far from clear. In the present work, the mixing flow of a sonic transverse jet injection in a supersonic cavity combustor is numerically investigated at two typical inflow velocities. The basic flow structures, unsteady flow dynamics, average flow structures, and several significant mixing performance parameters are well captured and compared based on high-resolution large eddy simulation. The simulation results show that separation shock induced by the jet is gradually merged with the bow shock at low Mach inflow so that the curved shock flow patter is produced. In addition, smaller large-scale coherent structures at the windward side and slower large-scale vortex transport are observed at low Mach inflow. At low Mach inflow, moreover, much narrower range of jet species mass fraction distributions and more upstream large-scale vortices breakdown and dissipation can be observed. The low Mach inflow generates weaker pair of counter-rotating vortices and some trailing counter-rotating vortices, which primarily leads to the weaker jet/cavity interaction. The baroclinic term effects are considerably weaker at low Mach inflow in the near field. In view of mixing efficiency and flammability efficiency, the effect of the cavity in enhancing mixing is more evident at low Mach inflow.

Tidal turbulence in medium depth water, primarily a model study

Tidal energy is considered to be one important future source of renewable energy. There is presently a strong development in new technology, and there is an emerging need to e.g., describe the turbulence intensity and its characteristics in a tidal stream. In this study we consider a high resolution Large Eddy Simulation (LES) in water with 80 m depth and a tidal stream with a maximum volume mean flow amplitude of 2 ms-1. the simulation is designed to describe turbulence characteristics at a developer site outside Holyhead in the Irish Sea. We find that the turbulence intensity and characteristics has clear time dependence, and that it is 100% stronger on the retarding tidal current as compared to the accelerating tidal current. We also find that it depends on the distance from the bottom. The turbulence is highly anisotropic with much longer length scales in the flow directions than perpendicular to flow direction. The simulation setup and results for mean flow quantities and turbulence measures are discussed in the presentation. Finally, results are compared with results from a ship mounted ADCP for mean flow characteristics and for turbulence quantities.

Numerical analysis on the transom-stern wake with a horizontal plunging jet

The turbulent flow behind a dry-transom stern with a plunging water jet is numerically studied. High-resolution large eddy simulation (LES) is performed to predict the wave-elevation topology and vortex structure in the wake with varying jet height. The theoretical impact position between jet flow and stern wave is proposed. The turbulent wake under the stern-jet configuration can be divided as converging-corner-wave region (CCW), mixing region (MR), transition region (TR) and developed region (DR). High-speed plunging jet speeds up the averaged-axial velocity and enhances the shear effect near the free surface. The upward movement of the rooster tail is suppressed by the parabolic jet flow, and periodical large scale air pockets are clearly observed following the wake angle along the downstream direction. Air pocket vortices and jet vortices are merging in the near wake and forming U-shaped vortex structures. Reducing jet height accelerates the instability of coherent vortex structure and energy dissipation in the developed region. The main contributions in the power spectra density (PSD) spectrum of Turbulent Kinetic Energy appear in the frequency range of 10–20 Hz with the evolution of wake vortices.

Stable Boundary Layers and Subfilter-Scale Motions

Recent high-resolution large-eddy simulations (LES) of a stable atmospheric boundary layer (SBL) with mesh sizes N=(5123,10243,20483) or mesh spacings ▵=(0.78,0.39,0.2) m are analyzed. The LES solutions are judged to be converged based on the good collapse of vertical profiles of mean winds, temperature, and low-order turbulence moments, i.e., fluxes and variances, with increasing N. The largest discrepancy is in the stably stratified region above the low-level jet. Subfilter-scale (SFS) motions are extracted from the LES with N=20483 and are compared to sonic anemometer fields from the horizontal array turbulence study (HATS) and its sequel over the ocean (OHATS). The results from the simulation and observations are compared using the dimensionless resolution ratio Λw/▵f where ▵f is the filter width and Λw is a characteristic scale of the energy-containing eddies in vertical velocity. The SFS motions from the observations and LES span the ranges 0.1<Λw/▵f<20 and are in good agreement. The small, medium, and large range of Λw/▵f correspond to Reynolds-averaged Navier–Stokes (RANS), the gray zone (a.k.a. “Terra Incognita”), and fine-resolution LES. The gray zone cuts across the peak in the energy spectrum and then flux parameterizations need to be adaptive and account for partially resolved flux but also “stochastic” flux fluctuations that represent the turbulent correlation between the fluctuating rate of strain and SFS flux tensors. LES data with mesh 20483 will be made available to the research community through the web and tools provided by the Johns Hopkins University Turbulence Database.

Water surface response to turbulent flow over a backward-facing step

The water surface response to subcritical turbulent flow over a backward-facing step (BFS) is studied via high-resolution large-eddy simulation (LES). The LES method is validated first using data of previously reported experiments. The LES-predicted water surface is decomposed into different types of gravity waves as well as turbulence-driven forced waves. Analysis of the LES data reveals the interplay between low-frequency large-scale turbulence structures, which are the result of flow separation from the step and reattachment behind the step, and the dynamics of the water surface. The water surface deformation is mainly the result of freely propagating gravity waves and forced waves, owing to turbulence in the form of rollers and/or hairpin vortices. Gravity waves with zero group velocity define the characteristic spatial and temporal scales of the surface deformations at higher frequencies, while large eddies determine their low-frequency modulation. These deformations are mainly confined in lateral bands that propagate downstream following the advection of the near-surface streamwise vortices (rollers) that are shed from the step. Steeper surface waves are observed in regions of negative perturbation velocity gradient and down-welling, downstream of the larger rollers, and are associated with thin isolated regions of high vorticity near the surface. The investigation of such a complex flow has shown that the decomposition of the water surface fluctuations into its different physical components may be used to identify the dynamics of the underlying flow structure.

Evaluation of Pulse Aerosol Forcing on Marine Stratocumulus Clouds in the Context of Marine Cloud Brightening

Abstract We explore the effect of aerosol perturbations on stratocumulus clouds in the context of marine cloud brightening (MCB) using high-resolution large-eddy simulations. We use a Lagrangian cloud microphysical model with a very detailed treatment of aerosol activation and droplet growth. The aerosol forcing is represented as a finite-width rectangular pulse in time (uniform in space). We analyze three stratocumulus cloud systems differing in their surface precipitation rate: namely, nonprecipitating, intermediate, and precipitating. We report on the diurnal evolution of these cloud systems subjected to a range of perturbations characterized by varying the amplitude and duration of the aerosol forcing pulse. Our simulations show that in the nonprecipitating system, the clouds are relatively insensitive to duration and amplitude, and are sensitive only to the total number concentration of the injected aerosol. In contrast, the precipitating cloud system is affected by the duration and the amplitude of the forcing, with the sensitivity conditional on the state of the cloud system before the injection of aerosol particles. We use these case studies to assess the efficacy of potential MCB spraying strategies. Our analysis shows that negative LWP adjustments offset a substantial fraction of the Twomey-induced brightening in all three cloud systems. This is countered by substantial cloud brightening obtained through precipitation-suppression-induced cloud-fraction adjustments.

Forecasting day-ahead 1-minute irradiance variability from numerical weather predictions

Accurate forecasts of solar irradiance are required for the large-scale integration of solar photovoltaic (PV) systems. Fluctuations of energy generation in the order of minutes can lead to issues on the electricity grid, therefore reliable forecasts of minute-to-minute irradiance variability are required. However, state of the art numerical weather predictions (NWP) deliver forecasts at a much coarser temporal resolution, e.g. hourly, missing crucial information on meteorological variability such as clouds. In this work we present a methodology to forecast minute-to-minute irradiance variability in terms of its probability density function (PDF) based on hourly NWP results, by applying statistical postprocessing using machine learning. The algorithm is tested using the 2.5 × 2.5 km2 HARMONIE-AROME (HA) mesoscale model as input, with 1-minute irradiance observations for 18 meteorological stations throughout the Netherlands used as a ground truth. The applicability of the algorithm to 31 × 31 km2 global-scale models is investigated using ERA5 reanalysis data, which yields comparable accuracies. We find that almost half of the inaccuracy of the postprocessed result is due to errors in the radiation forecast of the NWP model used as input. Finally, the proposed post-processing algorithm is compared to the next generation weather models based on high resolution Large Eddy Simulation (LES), at 75 m horizontal grid spacing, on a case study spanning four days. While LES underestimates values of high irradiance due to lack of 3D radiative effects, it enables detailed analysis of cloud and irradiance dynamics at high spatial and temporal resolution unreachable by statistical postprocessing.

Large-Eddy Simulations of wind turbine wakes in sheared inflows

Modern-day wind turbines are growing continuously in size and reach diameters of more than 200m in an effort to meet the fast growing demand for wind energy. As a consequence, the rotors are exposed to larger velocity variations in the approach flow due to the presence of shear, veer and turbulence. The shear of the ambient flow is an important effect that can impact the wake of a turbine twofold: one way is how the wake evolves in the sheared flow; the other way is by impacting the performance and loading of the turbine and, hence, the wake it produces. Both ways can affect the size, shape, spreading and recovery of the turbine wake and, consequently, impact on loads and power output of turbines located downstream. In this study, we analyzed the influence of different inflow wind shear configurations on the evolution of the wake behind the IEA 15MW reference wind turbine by means of high-resolution Large-Eddy Simulations. In order to isolate the shear effects, the mean and hub height wind speed of the inflow was kept constant by prescribing linear shear profiles without turbulence. The influence of Coriolis forces and thermal stratification are neglected. In addition, the effect of the imposed shear on the turbine’s power and thrust, and the effect of including the nacelle in the simulation, were monitored.

Evaluation of energy balance closure adjustment and imbalance prediction methods in the convective boundary layer – A large eddy simulation study

The non-closure of the surface energy balance is one of the greatest challenges in quantifying the atmosphere-surface exchange of energy and water. One open question associated with the energy imbalance is how to partition the residual energy, i.e., the difference between the available energy and the sum of turbulent fluxes, between the sensible and latent heat fluxes. Here, based on high-resolution large-eddy simulations (LESs), five energy balance closing methods and three imbalance prediction methods are evaluated in the convective boundary layer over idealized heterogeneous surfaces. The results show that advection fluxes are highly correlated with flux imbalances and are leading factors for the flux imbalances. Overall, the Bowen ratio closure method has a better performance than other closure methods, especially when the vertical advection flux dominates the flux imbalance where its assumption is nearly fulfilled. However, when the horizontal advection flux dominates the flux imbalance, the Bowen ratio closure method cannot correctly close the sensible and latent heat fluxes, even though it exhibits better performance than other methods. This is mainly because the heat and water vapor transported by horizontal advection originate from different sources due to surface heterogeneity, which breaks the assumption of the Bowen ratio closure method, leading to failure. Moreover, using the footprint-weighted surface true fluxes (weighted surface true fluxes within the source area of EC) calculated by the Lagrangian particle model instead of the analytical footprint models can reduce the flux imbalance and improve the performance of different closure methods. None of the existing imbalance prediction methods can correctly predict the flux imbalance for H or LE, even though the prediction method proposed over heterogeneous surfaces has a better performance than those proposed over homogeneous surfaces. Our findings provide meaningful suggestions for the selection of energy balance closing methods in practice.

Experimental and LBM analysis of medium-Reynolds number fluid flow around NACA0012 airfoil

PurposeThe purpose of this paper is the examination of fluid flow around NACA0012 airfoil, with the aim of the numerical validation between the experimental results in the wind tunnel and the Lattice Boltzmann method (LBM) analysis, for the medium Reynolds number (Re = 191,000). The LBM–large Eddy simulation (LES) method described in this paper opens up opportunities for faster computational fluid dynamics (CFD) analysis, because of the LBM scalability on high performance computing architectures, more specifically general purpose graphics processing units (GPGPUs), pertaining at the same time the high resolution LES approach.Design/methodology/approachProcess starts with data collection in open-circuit wind tunnel experiment. Furthermore, the pressure coefficient, as a comparative variable, has been used with varying angle of attack (2°, 4°, 6° and 8°) for both experiment and LBM analysis. To numerically reproduce the experimental results, the LBM coupled with the LES turbulence model, the generalized wall function (GWF) and the cumulant collision operator with D3Q27 velocity set has been used. Also, a mesh independence study has been provided to ensure result congruence.FindingsThe proposed LBM methodology is capable of highly accurate predictions when compared with experimental data. Besides, the special significance of this work is the possibility of experimental and CFD comparison for the same domain dimensions.Originality/valueConsidering the quality of results, root-mean-square error (RMSE) shows good correlations both for airfoil’s upper and lower surface. More precisely, maximal RMSE for the upper surface is 0.105, whereas 0.089 for the lower surface, regarding all angles of attack.

Aerodynamic noise due to complex internal flow through cordless vacuum cleaner and suction tower station

Although the demands and sales of cordless vacuum cleaner are on the rise in the global home appliance markets, consumers face the inconvenience of short battery life and frequent emptying of the dust box. To solve this inconvenience, a station tower that can automatically charge the battery and empty the dust box has been developed. However, aerodynamic noise generated when the station tower sucks dust causes another inconvenience. The purpose of this study is to identify the major aerodynamic noise sources that occur when such a station tower is connected to a wireless vacuum cleaner and operate, and to develop a low-noise design based on this. First, the entire flow path of a cordless vacuum cleaner and a station tower was simulated using the unsteady compressible RANS equations. Then, the main aerodynamic noise sources were identified using the vortex sound sources. From these results, the flow region through the head throat of the cordless vacuum cleaner was identified one of the most significant aerodynamic noise sources. Based on the identified noise source mechanism, new throat design was proposed, and its validity was investigated using a high-resolution Large Eddy Simulation technique. It was found that the strength of vortex sound source of pipe flow through the new head throat was much less than the original one. Finally, the new design geometry was applied to create a prototype, and the sound pressure spectrum measured for the prototype was compared to the original, which showed that the radiated noise level of the new one was less than the original one.

Sources of Stochasticity in the Growth of Cloud Droplets: Supersaturation Fluctuations versus Turbulent Transport

Abstract The role played by fluctuations of supersaturation in the growth of cloud droplets is examined in this study. The stochastic condensation framework and the three regimes of activation of cloud droplets— namely, mean dominant, fluctuation influenced, and fluctuation dominant—are used for analyzing the data from high-resolution large-eddy simulations of the Pi convection-cloud chamber. Based on a detailed budget analysis the significance of all the terms in the evolution of the droplet size distribution equation is evaluated in all three regimes. The analysis indicates that the mean-growth rate is a dominant process in shaping the droplet size distribution in all three regimes. Turbulence introduces two sources of stochasticity, turbulent transport and particle lifetime, and supersaturation fluctuations. The transport of cloud droplets plays an important role in all three regimes, whereas the direct effect of supersaturation fluctuations is primarily related to the activation and growth of the small droplets in the fluctuation-influenced and fluctuation-dominant regimes. We compare our results against the previous studies (experimental and theory) of the Pi chamber, and discuss the limitations of the existing models based on the stochastic condensation framework. Furthermore, we extend the discussion of our results to atmospheric clouds, and in particular focus on recent adiabatic turbulent cloud parcel simulations based on the stochastic condensation framework, and emphasize the importance of entrainment/mixing and turbulent transport in shaping the droplet size distribution.

Row spacing as a controller of solar module temperature and power output in solar farms

When the temperature of solar photovoltaic modules rises, efficiency drops and module degradation accelerates. The spatial arrangement of solar modules can affect convective cooling and, consequently, module temperatures. However, the impact of row spacing on convective cooling in realistic solar farms has not yet been studied. Here, we develop six solar farm arrangements consisting of a fixed number of rows with varying streamwise row spacing. We model the flow and heat transfer of each solar farm using high-resolution large-eddy simulations. Results indicate that increasing row spacing can enhance convective cooling by 14.8%, which reduces module temperature by 6.6 °C and increases power output by 4.0% on average.

Combining Phi6 as a surrogate virus and computational large-eddy simulations to study airborne transmission of SARS-CoV-2 in a restaurant.

COVID-19 has highlighted the need for indoor risk-reduction strategies. Our aim is to provide information about the virus dispersion and attempts to reduce the infection risk. Indoor transmission was studied simulating a dining situation in a restaurant. Aerosolized Phi6 viruses were detected with several methods. The aerosol dispersion was modeled by using the Large-Eddy Simulation (LES) technique. Three risk-reduction strategies were studied: (1) augmenting ventilation with air purifiers, (2) spatial partitioning with dividers, and (3) combination of 1 and 2. In all simulations infectious viruses were detected throughout the space proving the existence long-distance aerosol transmission indoors. Experimental cumulative virus numbers and LES dispersion results were qualitatively similar. The LES results were further utilized to derive the evolution of infection probability. Air purifiers augmenting the effective ventilation rate by 65% reduced the spatially averaged infection probability by 30%-32%. This relative reduction manifests with approximately 15 min lag as aerosol dispersion only gradually reaches the purifier units. Both viral findings and LES results confirm that spatial partitioning has a negligible effect on the mean infection-probability indoors, but may affect the local levels adversely. Exploitation of high-resolution LES jointly with microbiological measurements enables an informative interpretation of the experimental results and facilitates a more complete risk assessment.

Exploring Satellite-Derived Relationships between Cloud Droplet Number Concentration and Liquid Water Path Using a Large-Domain Large-Eddy Simulation

Important aspects of the adjustments to aerosol-cloud interactions can be examined using the relationship between cloud droplet number concentration (N_d) and liquid water path (LWP). Specifically, this relation can constrain the role of aerosols in leading to thicker or thinner clouds in response to adjustment mechanisms. This study investigates the satellite retrieved relationship between N_d and LWP for a selected case of mid-latitude continental clouds using high-resolution Large-eddy simulations (LES) over a large domain in weather prediction mode. Since the satellite retrieval uses the adiabatic assumption to derive the N_d, we have also considered adiabatic N_d (N_Ad) from the LES model for comparison. The joint histogram analysis shows that the N_Ad-LWP relationship in the LES model and the satellite is in approximate agreement. In both cases, the peak conditional probability (CP) is confined to lower N_Ad and LWP; the corresponding mean LWP (LWP) shows a weak relation with N_Ad. The CP shows a larger spread at higher N_Ad (>50 cm^–3), and the LWP increases non-monotonically with increasing N_Ad in both cases. Nevertheless, both lack the negative N_Ad-LWP relationship at higher N_Ad, the entrainment effect on cloud droplets. In contrast, the model simulated N_d-LWP clearly illustrates a much more nonlinear (an increase in LWP with increasing N_d and a decrease in LWP at higher N_d) relationship, which clearly depicts the cloud lifetime and the entrainment effect. Additionally, our analysis demonstrates a regime dependency (marine and continental) in the N_Ad-LWP relation from the satellite retrievals. Comparing local vs large-scale statistics from satellite data shows that continental clouds exhibit only a weak nonlinear N_Ad-LWP relationship. Hence a regime-based N_d-LWP analysis is even more relevant when it comes to warm continental clouds and their comparison to satellite retrievals.