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DOE OSTI2025

Evaluating Entrainment–Mixing Characteristics through Direct Comparisons of Drop Size Distributions Using In Situ Observations from ACE-ENA

Abstract Constraining the impacts of entrainment and associated mixing (i.e., entrainment–mixing) on cloud properties continues to be difficult, partly due to observational uncertainties as well as a lacking consensus of which methodologies for diagnosing entrainment–mixing are most appropriate. This study introduces a novel method to evaluate the presence and degree of inhomogeneous and homogeneous mixing using ∼100 h of in situ observations from a research aircraft over the northeastern Atlantic. Specifically, drop size distributions are compared between regions containing negligible and significant entrainment for select flight legs, making a direct characterization of the degree of homogeneous and inhomogeneous mixing possible. A measure of drop concentration variance is used as a proxy variable to diagnose entrainment–mixing. Results correspond well with entrainment–mixing metrics, showing lower Damköhler numbers where drop size distributions shift toward smaller drop sizes (i.e., inhomogeneous mixing) and greater transition length scales where drop size distributions do not (i.e., homogeneous mixing). Inhomogeneous mixing occurs in most samples from Aerosol and Cloud Experiment in the Eastern North Atlantic (ACE-ENA) (regardless of homogeneous mixing frequencies increasing with increasing spatial resolution from ∼100 to ∼10 m) and is associated with decreased drop size relative dispersion and both greater aerosol and drop concentrations compared with homogeneous mixing. Precipitating clouds have a greater frequency of homogeneous mixing compared with nonprecipitating clouds. The proposed methodology is similarly applied to in situ observations of southeast Pacific stratocumulus, shallow convective clouds over central Oklahoma and low-level clouds over the Southern Ocean. All four locations are primarily dominated by inhomogeneous mixing with minimal variability among each region.

Clouds↗

DOE OSTI2025

Convergence of Cloud Droplet Spectral Relative Dispersion During Entrainment‐Mixing Based on Particle‐Resolved Direct Numerical Simulations

Entrainment-mixing processes critically impact cloud microphysical properties, but their effects on the relative dispersion (d) of cloud droplet size distributions (CDSDs) remain elusive. A direct numerical simulation model is initialized with different CDSDs to fill the gap. These results show that d decreases for broad CDSDs and increases for narrow ones, ultimately converging to approximately 0.5 regardless of initial CDSDs during the evaporation-dominated mixing stage. The supersaturation fluctuation and the shape of CDSDs jointly influence the convergence behavior of d. Further sensitivity tests show that the initial microphysical/dynamical/thermodynamical conditions exert negligible effects on the final converged value of d but affect the convergence rate (k). The k generally increases with increasing droplet number concentration and dissipation rate, and increases with decreasing liquid water content, relative humidity of entrained air, and mixing fraction of cloudy air. A conceptual model with two timescales is proposed; k and the timescales are negatively correlated, meaning that slow mixing and/or evaporation process results in slow convergence of d. In conclusion, this finding provides an important reference for improving understanding and parameterization of d during the entrainment-mixing processes.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1990

Laboratory experiments on stability and entrainment of oceanic stratocumulus. Part 2: Entrainment experiment

A stratified interface is stable to the buoyancy reversal instability for surprisingly large values of D (buoyancy reversal parameter). A new instability mechanism is proposed, which considers the mixing process at the interface. For the type of density curves studied here, under strong perturbations, the mixed parcel must have a buoyancy reversal comparable to the initial stratification before the interface is unstable. This is in accord with a simple model of the interface mixing process, as well as aircraft observations of long-live marine stratocumulus clouds. These clouds' remarkable longevity in the face of finite D indicates that they can be stable (Hanson, 1984; Albrecht et al., 1985; Siems et al., 1989). It is suggested that buoyancy reversal as well as the disturbance must be large for Cloudtop Entrainment Stability. The effect of buoyancy reversal (evaporative cooling) does not always enhance the entrainment rate over that in the inert case, but it may be negligible if Ri (Richardson number) is large (Ri is larger than 50) and D is small (D is smaller than 0.5). This work may shed some light on the fundamental mechanism of the breakup process of the subtropical stratocumulus clouds into tradewind cumulus. These results may also be related to the instability in the Weddell Sea off of Antarctica.

Shy, Shenqyang S.↗

DOE OSTI2024

The Dual Nature of Entrainment-Mixing Signatures Revealed through Large-Eddy Simulations of a Convection-Cloud Chamber

Abstract Entrainment of subsaturated air into a cloud can influence its optical and microphysical properties in various ways, depending on the droplet evaporation and turbulent mixing time scales. Previous experiments in the Pi convection-cloud chamber have revealed that, given a fixed entrained air property, the mixing of entrained subsaturated air results in complete evaporation of some cloud droplets, with the rest remaining unchanged. This is a signature of inhomogeneous mixing. While comparing the results of entrainment with varying air properties, the mixing signature appears as if the subsaturated air is well mixed with the cloud to evenly reduce the droplets’ size. In other words, taken together, the experiments appear to have the signature of homogeneous mixing. To explore these results in a greater depth, we conduct large-eddy simulations combined with a bin microphysics scheme. Our results reproduce the similar signatures of inhomogeneous and homogeneous mixing, implying that LES can resolve the inhomogeneous mixing when the grid spacing is smaller than the entrained air parcel. Additionally, we observe that increasing the aerosol injection rate enhances the signature of inhomogeneous mixing, while coarser grid spacing diminishes it. Finally, the change in wall fluxes in response to various entrained air properties confirms that the homogeneous signature seen in the analysis of an ensemble of simulations is the result of various equilibrium states. This further strengthens the suggestion that the homogeneous mixing signature found in aircraft observations near the cloud top may result from combining entrainment events of different intensities, possibly caused by various-sized eddies. Significance Statement Large-eddy simulation and size-resolved microphysics can resolve time scales for turbulent mixing and evaporation and, therefore, are well suited for reproducing, extending, and interpreting the entrainment experiment in the Pi convection-cloud chamber. Our simulation results confirm (i) the inhomogeneous mixing signature for an individual entrainment event and (ii) the appearance of homogeneous mixing in an ensemble of entrainment episodes. Furthermore, we demonstrate that the inhomogeneous mixing signature is more pronounced in a polluted cloud, but coarser grid spacing in simulations may compromise the accuracy of this signature. Last, the homogeneous mixing signature results from various equilibrium states established for different entrainment intensities and adjusted wall fluxes, which are challenging to measure experimentally but can be easily analyzed in the simulations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

A large-eddy simulation exploration of the assumptions used in retrieving entrainment from a mixing diagram approach with ground-based remote sensors

Entrainment is a crucial component of the atmospheric boundary layer (BL) moisture and heat budget. While usually thought of as only entrainment flux, entrainment within the mixed layer budget equation is really composed of two terms: the flux of a property across the boundary separating the BL from the free troposphere and the change in the concentration of a property as the depth of the BL changes. In a recent study, Wakefield et al. (2023) used ground-based remote-sensing observations to estimate entrainment flux as the residual of a mixing diagram framework that was applied to the daytime convective boundary layer. This present work uses large-eddy simulation (LES) to examine how well this residual assumption for entrainment fluxes alone compares to the actual sum of those two entrainment terms derived from spatial averages of the LES output. We highlight the importance of the second entrainment term in closing the mixed layer budget and show that the residual assumption does not represent entrainment flux only but rather a total entrainment term when the boundary layer depth is changing.

Rosenberger, Tessa E. [Cleveland State Univ., Clev↗

NASA NTRS1994

Ifluence of crystallization and entrainment of cooler material on the emplacement of basaltic aa lava flows

A theoretical model is used to describe and investigate the effects of simultaneous crystallization, radiation loss, and entrainment of cooler material on the temperature of a well-mixed core of an active aa lava flow. Entrainment of crust, levee debris, and base material into the interior of active flows has been observed, but the degree of assimilation and the thermal consequences are difficult to quantify. The rate of entrainment can be constrained by supplementing the theoretical model with information on the crystallization along the path of the flow and estimation of the radiative loss from the flow interior. Application of the model is demonstrated with the 1984 Mauna Loa flow, which was erupted about 30 C undercooled. Without any entrainment of cooler material, the high crystallization rates would have driven temperatures in the core wall above temperatures measured by thermocouple and estimated from glass geothermometry. One plausible scenario for this flow, which agrees with available temperature and crystallinity measurements, has a high initial rate of entrainment during the first 8 hours of travel (a mass ratio of entrained material to fluid core of about 15% if the average temperature of the entrained material was 600 C), which counterbalances the latent heat from approximately 40% crystallization. In this scenario, the model suggests an additional 5% crystallization and a 5% entrainment mass ratio over the subsequent 16-hour period. Measurements of crystallization, radiative losses, and entrainment factors are necessary for understanding the detailed thermal histories of active lava flows.

Crisp, Joy↗

NASA NTRS1982

Clouds and entrainment

The concept of entrainment is discussed, and the knowledge that has been acquired about entraining turbulence in clear air is surveyed. Attention is then given to observations and models of stratocumulus entrainment, which show some of the ways in which cloudiness modifies the entrainment process. Entraining cumuli are also considered, with some of the differences between cumulus entrainment and stratocumulus entrainment noted. Emphasis is placed on the dynamical aspects of entrainment; its effects on droplet spectra and other microphysical aspects are mentioned only briefly.

Randall, D. A.↗

NASA NTRS1984

Can cloud-top entrainment promote cloud growth?

The primary significance of Cloud Deepening through Entrainment (CDE) is that it can prevent the cloud top entrainment instability from destroying a cloud deck. Without suppressing the instability, CDE transforms it from a cloud destroyer to a cloud builder. The analysis does not depend on an entrainment hypothesis. Moreover, it is not restricted to PBL stratocumulus sheets. Stratiform clouds in the free atmosphere can be subject to CDE we need only reinterpret Ps as the pressure at the base of an elevated turbulent mixed layer. Modest departures from well mixedness will alter the results quantitatively but not qualitatively. Processes other than entrainment, such as surface evaporation, radiative cooling, and advection will often work with CDE to build a cloud layer; but of course they can also oppose CDE by reducing the relative humidity. If we make the weak assumption that the deepening of a cloud layer favors an increase in the cloud top entrainment rate (without specifying any particular functional relationship) we are led to speculate that CDE can cause runaway cloud growth, even in the absence of cloud top entrainment instability. through CDE entrainment leads to a deeper cloud, which leads to stronger entrainment.

Randall, D. A.↗

NASA NTRS1998

A Quantitative Investigation of Entrainment and Detrainment in Numerically Simulated Convective Clouds: Simulations of Cumulonimbus Clouds - Pt. 2

Deep cumulonimbus clouds are simulated using a model that makes accurate diagnoses of entrainment and detrainment rates and of the properties of entrained and detrained air. Clouds generated by a variety of initial thermodynamic soundings are compared. In the simulations, updraft entrainment rates are large near and above cloud base, through the entire depth of the conditionally unstable layer. Stronger updrafts in a more unstable environment are better able to entrain relatively undisturbed environmental air, while weaker updrafts can entrain only air that has been modified by the clouds. When the maximum buoyancy is large, the updraft includes parcels with a wide range of buoyancies, while weaker clouds are more horizontally uniform. Strong downdrafts originate from levels at which updrafts detrain, and their mass flux depends on the mass flux of the updraft. The magnitude of mixing between cloud and environment, not the entrainment rate, varies inversely with the cloud radius. How much of the mixed air is entrained depends on the buoyancy.

Cohen, Charles↗

DOE OSTI2025

The Effect of Updraft Entrainment on Convective Cell Deepening in Realistic Large-Eddy Simulations

Entrainment of surrounding cooler and drier air into convective updrafts is one of the key processes that influence deep convection initiation and growth. Numerous studies have investigated the effect of entrainment on isolated convective cloud growth in idealized simulations, but the importance of this effect in realistic conditions with many interacting convective clouds remains uncertain. We examine the impact of entrainment on the depth reached by convective clouds in realistic large-eddy simulations (LES) over central Argentina during the Cloud, Aerosol, and Complex Terrain Interactions (CACTI) field campaign. Cloudy updrafts and their associated properties are assigned to convective cells tracked with radar reflectivity signatures. Several thousand convective cells are tracked over two high convective available potential energy (CAPE) and two low CAPE cases that support cells of varying depths and intensities. Entrainment is calculated explicitly as the fluxes of air into the outer surface of each cloudy updraft. Single-predictor logistic regression models are used to determine the relative importance of updraft, near-updraft, and preconvective initiation atmospheric conditions in predicting whether convective cells become deep. We then build a multiple-predictor regression model pairing important updraft and meteorological metrics with fractional entrainment rate. The probability of cells transitioning to deep convection is most sensitive to ambient 600-hPa relative humidity (42% of total metric contribution to cloud depth predictability), followed by low-level CAPE (28%), cloud-base updraft width (19%), and fractional entrainment (11%). Thus, the initial width of the updraft along with potential buoyancy and its dilution through the midtroposphere collectively determine whether deep convection will result from shallower clouds.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Quantifying the Turbulent Entrainment‐Mixing Processes Based on Z ‐LWC Relationships of Cloud Droplets

Abstract Turbulent entrainment‐mixing processes profoundly influence the relationship between radar reflectivity factor and liquid water content ( Z ‐LWC) of cloud droplets. However, quantification of the entrainment‐mixing mechanisms based on the Z ‐LWC relationship is still lacking. To address this gap, 12,218 entrainment‐mixing cases are simulated using the Explicit Mixing Parcel Model. We examine the variations of the parameters in the power‐law relationship Z = a LWC b , and the relationship between parameter b and homogeneous mixing degree ( ψ ), a measure quantifying entrainment‐mixing processes. The results indicate that parameter b distributes within the range of 1–2, with a positive correlation between parameter b and ψ . The b ‐ ψ relationship is fitted, which connects the Z ‐LWC relationship for various entrainment‐mixing types. The results suggest the potential for employing a remote sensing approach to investigate the entrainment‐mixing mechanisms of non‐precipitating small cumulus/stratocumulus clouds, thereby overcoming the limitations of traditional observational studies that rely solely on aircraft observations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Towards retrieving cloud top entrainment velocities from MISR cloud motion vectors

Although important, direct retrievals of entrainment rates in cloud-topped planetary boundary layer (PBL) remain elusive. Here we present a novel technique for retrieving cloud-top entrainment velocities using only Multi-angle Imaging Spectro-Radiometer (MISR) stereoscopic retrievals of cloud-motion vectors (CMVs) and cloud-top heights (CTHs). Mesoscale vertical air velocity at CTH is diagnosed from the continuity equation and then used to derive entrainment velocities from the PBL mass-budget equation. The algorithm is demonstrated through a case of marine stratocumulus deck off the California coast, with comparisons made against data from the European Centre for Medium-range Weather Forecasts (ECMWF) reanalysis (ERA5) and the data from other satellites. MISR low-cloud CTH for this case were lower than the ERA5 reported PBL depth by 189 ± 87 m. These differences in cloud top heights partly modulate the differences in the ERA5 and MISR horizontal winds, with larger differences in meridional over zonal wind components. Average difference between ERA5 and MISR derived mesoscale vertical air motion at cloud top was 0.14 ± 0.73 cm s −1 , while the same for entrainment rate was −0.09 ± 0.46 cm s −1 . The uncertainties in the utilized CTHs and CMVs are propagated to derive systematic and random retrieval uncertainties. Fractional uncertainty is lower than 25 % when the retrieved mesoscale vertical air motion is stronger than ±0.04 cm s −1 and entrainment velocities are stronger than ±0.03 cm s −1 . These results showcase the ability to derive mesoscale vertical air motion and entrainment rates from MISR observations and motivate its extension to generate a global climatology leveraging its full 23-year record (2000–2022). Nonetheless comprehensive validation of the retrievals is warranted through comparisons with estimates from an independent dataset across diverse weather conditions.

Mitra, Arka [Argonne National Laboratory (ANL), Ar↗

NASA NTRS1979

Entrainment characteristics of unsteady subsonic jets

The effectiveness of jet unsteadiness in enhancing flow entrainment was assessed. It was conducted that entrainment depends on the type and amount of jet unsteadiness. Apparently, the mere introduction of jet unsteadiness by small sinusoidal flow angle variations is insufficient to enhance entrainment but, it should be noted that the results were obtained at measuring stations which are all many nozzle widths downstream of the jet nozzle. Thus, no fully conclusive statement can be made at this time about the entrainment close to the nozzle. The high entrainment of the fluidically oscillated jet was caused by the high-frequency content of this square wave type of oscillation but more detailed measurements are clearly needed, in particular for the fluidically oscillated and the pulsed jets. Practical ejector application requires the proper trade-off between entrainment and primary nozzle thrust efficiency.

Platzer, M. F.↗

NASA NTRS1982

Entrainment and detrainment in a simple cumulus cloud model

A cumulus cloud model, analogous to the mixed-layer models of the planetary boundary layer and the upper ocean, is developed using a single, unitary entrainment process in which the motion of the cloud boundary relative to the mean flow is permitted, produced, and controlled by turbulent processes. An alternate theory to the mixing-length theory of Asai and Kasahara (1967) is proposed which completely removes the strong scale-dependence of the Asai-Kasahara model. The model reintroduces scale-dependence by introducing including the pe5turbation pressure term of the equation of vertical motion. It is shown that the model predicts deeper clouds than the Asai-Kasahara model for a given sounding, due to the entrainment assumption and the effects of the perturbation pressure. Lateral entrainment dominates cloud-top entrainment, although finite-difference errors increase the cloud-top entrainment rate from zero to a positive value in actual situations. The fractional entrainment rate for updrafts is determined to vary only slightly with height and to decrease only slowly as the cloud radius increases, while the fractional detrainment rate for updrafts increases with height.

Randall, D. A.↗

DOE OSTI2025

Implementation and Evaluation of Physics-Driven Dynamic Entrainment-Mixing Parameterization in a Climate Model and Its Impact on Low-Cloud Simulation

The turbulent entrainment-mixing process in the Community Earth System Model version 1.2 (CESM1.2) is assumed to follow the extremely inhomogeneous entrainment-mixing. However, different entrainment-mixing scenarios can occur in real clouds. To address this deficiency, a unifying parameterization that represents different entrainment-mixing processes is implemented and evaluated in CESM1.2. The results indicate that the homogeneous mixing degree values simulated by the new parameterization in CESM1.2 are predominantly greater than 50%, suggesting a tendency toward homogeneous mixing. Compared to the extremely inhomogeneous mixing mechanism, the new parameterization increases the cloud droplet number concentration (Nc). More importantly, the new parameterization improves low-cloud fraction (CLDLOW) simulation in Northwest Pacific (NWP) and Southeast Pacific (SEP) regions, with relative improvements of 2.95% and 4.17%, respectively. Furthermore, the improvements reach up to 44.6% and 16.2% in the NWP and SEP regions, respectively, when considering the relationship between N c and CLDLOW. Further analysis reveals that the new parameterization enhances cloud optical depth, longwave radiative cooling effect, net condensation rate, cloud water mixing ratio, lower-troposphere stability, and CLDLOW by increasing N c . Additionally, these results underscore the importance of improving entrainment-mixing parameterization in climate models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Shallow cumulus entrainment: observational retrieval, physical interpretation, and climate impacts (Final grant report)

This document constitutes a final technical report for DE-SC0020083, a research grant awarded by the US Department of Energy Office of Science, to Prof. Daniel Kirshbaum at McGill University. The original research proposal, entitled "Shallow cumulus entrainment: observational retrieval, physical interpretation, and climate impacts", defined four scientific objectives that synthesized ARM observations with turbulence-permitting large-eddy simulations (LES) to quantify and understand the process of cumulus entrainment, whereby a cumulus cloud ingests surrounding air through its lateral edges. These objectives included developing observational climatologies of cumulus bulk entrainment rate at two ARM observatories, physical interpretation of these findings using LES, quantification of the impacts of subcloud circulations on entrainment, and the climate impacts of flow-dependent entrainment variations. In the six years that have elapsed since the grant was awarded (three funded years and three no-cost annual extensions), all four of the objectives were successfully addressed. Four personnel were trained (one B.Sc., one M.Sc. to completion, five years of Ph.D. training, and 2.5 years of postdoctoral training), eight peer-reviewed articles were published in high-impact journals, and 20 presentations were delivered (three invited).

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1979

A numerical study of jet entrainment effects on the subsonic flow over nozzle afterbodies

A viscous-inviscid interaction model has been developed which accounts for jet entrainment effects in the prediction of the subsonic flow over nozzle afterbodies. The jet entrainment model is based on the concept of a weakly interacting shear layer in which the local streamline deflections due to entrainment are accounted for by a displacement-thickness type correction to the inviscid plume boundary. The entire flowfield is solved in an iterative manner to account for the effects on the inviscid external flow of the turbulent boundary layer, turbulent mixing and chemical reactions in the shear layer, and the inviscid jet exhaust flow. The individual components of the computational model are described and numerical results are presented which illustrate the interactive effects of entrainment on the overall flow structure. The validity of the interactive model is assessed by comparisons with data obtained from flowfield measurements on cold-air jet exhausts. Numerical results and experimental data are also given which show the entrainment effects on nozzle boattail drag under various jet exhaust and freestream flow conditions.

Wilmoth, R. G.↗

NASA NTRS1978

The entraining moist boundary layer

A unified theory of entrainment into the planetary boundary layer is presented. It is assumed that the rates of buoyant and shear production of turbulence kinetic energy can be determined in terms of the entrainment mass flux. An expression is derived from the conservation law for turbulence kinetic energy, which, with the introduction of an empirical parameter, can be used together with a second relation between turbulence kinetic energy and the turbulence velocity scale to obtain the mass entrainment flux. The theory provides descriptions of storage-limited entrainment, buoyancy-limited entrainment into a clear mixed layer, and shallowing. It has been incorporated into a simulation of Day 33 of the Wangara experiment using a simple mixed layer model.

Randall, D. A.↗