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At least 19 records

A New 1D Model for Thermal Mixing and Stratification in Advanced Reactor Transients

Thermal mixing and stratification in large pools and enclosures play a critical role in the safety and performance of pool-type nuclear reactors, particularly during transient scenarios involving significant temperature differences between incoming and bulk coolant. Accurate modeling of these phenomena is essential for predicting system behavior and supporting passive safety features such as natural circulation. Here, this paper presents a new 1D model for thermal mixing and stratification, developed and implemented in the SAM code. The model represents a large pool as 1D coolant jet channels and zero-dimensional bulk pool volumes, enabling the simulation of a wide range of flow configurations, including hot and cold jet interactions, stratified layers, and the influence of complex geometries such as ceilings, free surfaces, and internal obstacles. Heat exchange between jet and pool regions is governed by closure relations calibrated against 3D computational fluid dynamics (CFD) simulations. The model improves upon earlier approaches by incorporating time-dependent jet characteristics and capturing the associated delay effects more accurately. Code-to-code comparisons and validation against experimental data from the Thermal Stratification Test Facility demonstrate the model’s accuracy and flexibility. This work offers two key contributions: (1) an efficient and robust method for simulating thermal mixing and stratification at the system level, eliminating the need for external coupling between system analysis codes and CFD, and (2) a significant enhancement of SAM’s capabilities to analyze thermal stratification phenomena in advanced reactor systems.

SAM

High-Fidelity Simulation of the Light-to-Dense Stratification Transient in the HiRJET Facility

Density stratification in a large enclosure is a crucial phenomenon to heat transfer and sustainable passive heat removal of a sodium fast reactor during reactivity transients. However, engineering turbulence models were identified to have unsatisfactory performance in predicting propagation of a stratified front. Yet, the scarcity of high-resolution data for stratification hampers the development of models. To explor e applications of leveraging direct numerical simulation (DNS) data to support turbulence model development, this work conducted DNS using NekRS to study a long stratification transient in the High-Resolution Jet (HiRJET) experimental facility. Here, this work considers an experiment run where light fluid is injected into a tank containing a denser fluid with a relative density difference of 1.5%. Formation of the stratified layer is identified as impingement of the buoyant jet promoting mixing of the two fluids. Based on the transient statistics, transport of the concentration can be characterized by regions with dominating effects of turbulent mixing, buoyant dissipation, and molecular diffusion, respectively, as moving away from the elevation of jet impingement. Concentration near the stratified front also exhibits oscillation at Brunt-Väisälä frequency. Preliminary validation of the simulation showed encouraging agreement of the concentration distribution with the reference experiment.

buoyant mixing

The role of thermal stratification on the co‐spectral properties of momentum transport above an Amazonian forest

The influence of thermal stratification on the turbulent kinetic energy balance has been widely studied; however, its influence on the turbulent stress remains less explored in the presence of tall vegetated canopies and less ideal micrometeorological conditions. Here, the impact of thermal stratification on turbulent momentum flux is considered in the roughness sublayer (RSL) and the atmospheric surface layer (ASL) using the Amazon Tall Tower Observatory (ATTO) in Brazil. A scalewise co‐spectral budget (CSB) model is developed using standard closure schemes for the pressure–velocity decorrelation. The CSB revealed that the co‐spectrum ${F}_{wu}\left({k}_x\right)$ between longitudinal (u') and vertical (w') velocity fluctuations is impacted by the energy spectrum of the vertical velocity ${E}_{ww}\left({k}_x\right)$ and the much less studied longitudinal heat‐flux co‐spectrum ${F}_{u{\theta}_{\mathrm{v}}}\left({k}_x\right)$, where ${\theta}_{\mathrm{v}}^{\prime }$ are temperature fluctuations and ${k}_x$ is the longitudinal wavenumber. Under stable, very stable, and dynamic–convective conditions, the scaling exponent ${F}_{wu}\left({k}_x\right)$ in for the inertial subrange (ISR) scales is dominated by ${F}_{u{\theta}_{\mathrm{v}}}\left({k}_x\right)$ instead of ${E}_{ww}\left({k}_x\right)$. A near ${k}_x^{-7/3}$scaling in ${F}_{u{\theta}_{\mathrm{v}}}\left({k}_x\right)$ robust to large variations in thermal stratification is found, whereas the Kolmogorov ISR scaling for ${E}_{ww}\left({k}_x\right)\sim {k}_x^{-5/3}$ is not found. The scale‐dependent decorrelation time between u' and w' is dominated by ${\epsilon}^{-1/3}{k}_x^{-2/3}$ in the ISR, but is nearly constant for eddies larger than the vertical velocity integral scale, regardless of stability. Implications of these findings for generalized stability correction functions that are based on the turbulent stress budget instead of the turbulent kinetic energy budget are discussed.

canopy turbulence

Effects of stratification on overshooting and waves atop the convective core of M ⊙ main-sequence stars

As a massive star evolves along the main sequence, its core contracts, leaving behind a stable stratification in helium. We simulate two-dimensional convection in the core at three different stages of evolution of a $5\,\mathrm{ M}_{\odot }$ star, with three different stratifications in helium atop the core. We study the propagation of internal gravity waves in the stably stratified envelope, along with the overshooting length of convective plumes above the convective boundary. We find that the stratification in helium in evolved stars hinders radial motions and effectively shields the radiative envelope against plume penetration. This prevents convective overshooting from being an efficient mixing process in the radiative envelope. In addition, internal gravity waves are less excited in evolved models compared to the zero-age-main-sequence model, and are also more damped in the stratified region above the core. As a result, the wave power is several orders of magnitude lower in mid- and terminal-main-sequence models compared to zero-age-main-sequence stars.

79 ASTRONOMY AND ASTROPHYSICS

Evolution of oxygen and stratification and their relationship in the North Pacific Ocean in CMIP6 Earth system models

Abstract. This study examines the linkages between the upper-ocean (0–200 m) oxygen (O2) content and stratification in the North Pacific Ocean using four Earth system models (ESMs), an ocean hindcast simulation, and an ocean reanalysis. The trends and variability in oceanic O2 content are driven by the imbalance between physical supply and biological demand. Physical supply is primarily controlled by ocean ventilation, which is responsible for the transport of O2-rich surface waters to the subsurface. Isopycnic potential vorticity (IPV), a quasi-conservative tracer proportional to density stratification that can be evaluated from temperature and salinity measurements, is used herein as a dynamical proxy for ocean ventilation. The predictability potential of the IPV field is evaluated through its information entropy. The results highlight a strong O2–IPV connection and somewhat higher (as compared to the rest of the basin) predictability potential for IPV across the tropical Pacific, where the El Niño–Southern Oscillation occurs. This pattern of higher predictability and strong anticorrelation between O2 and stratification is robust across multiple models and datasets. In contrast, IPV at mid-latitudes has low predictability potential and its center of action differs from that of O2. In addition, the locations of extreme events or hotspots may or may not differ between the two fields, with a strong model dependency, which persists in future projections. On the one hand, these results suggest that it may be possible to monitor ocean O2 in the tropical Pacific based on a few observational sites co-located with the more abundant IPV measurements; on the other, they lead us to question the robustness of the IPV–O2 relationship in the extratropics. The proposed framework helps to characterize and interpret O2 variability in relation to physical variability and may be especially useful in the analysis of new observation-based data products derived from the BGC-Argo float array in combination with the traditional but far more abundant Argo data.

Novi, Lyuba

Effect of particle shape on stratification in drying films of binary colloidal mixtures

The role of particle shape in evaporation-induced auto-stratification in polydisperse colloidal suspensions is explored with molecular dynamics simulations of mixtures of spheres and aspherical particles. A unified framework based on the competition between diffusion and diffusiophoresis is proposed to understand the effects of shape and size dispersity. In general, particles diffusing more slowly (e.g., larger particles) tend to accumulate more strongly at the evaporation front. However, larger particles have larger surface areas and therefore greater diffusiophoretic mobility. Hence, they are more likely to be driven away from the evaporation front via diffusiophoresis. For a rapidly dried bidisperse suspension containing small and large spheres, the competition leads to “small-on-top” stratification. Here, we employ a computational model in which the diffusion coefficient is inversely proportional to particle mass. For a mixture of spheres and aspherical particles with similar mass, the diffusion contrast is reduced, and the spheres are always enriched at the evaporation front as they have the smallest surface area for a given mass and, therefore, the lowest diffusiophoretic mobility. Furthermore, for a mixture of solid and hollow spheres that have the same outer radius and thus the same surface area, the diffusiophoretic contrast is suppressed, and the system is dominated by diffusion. Consequently, the solid spheres, which have a larger mass and diffuse more slowly, accumulate on top of the hollow spheres. Finally, for a mixture of thin disks and long rods that differ significantly in shape but have similar mass and surface area, both diffusion and diffusiophoresis contrasts are suppressed, and the mixture does not stratify.

Classical molecular dynamic simulations

Bayesian Optimized Deep Ensemble for Uncertainty Quantification of Deep Neural Networks: a System Safety Case Study on Sodium Fast Reactor Thermal Stratification Modeling

Deep neural networks (DNNs) are increasingly important to scientific computing and engineering system simulations. Accurate uncertainty quantification (UQ) for DNNs is critical in safety-sensitive engineering domains. Traditional Deep Ensemble (DE) methods, while easy to implement, frequently suffer from poorly calibrated uncertainty estimates and limited predictive accuracy due to reliance on fixed architectures with varied weight initializations. To address these issues, we introduce a workflow that combines Bayesian Optimization (BO) and DE. The workflow is modular, scalable, and integrates parallel BO initialized with Sobol sequences to individually optimize the hyperparameters of each ensemble member. This method enhances ensemble diversity, improves predictive accuracy, and provides reliable uncertainty estimates. We evaluate the proposed BODE approach in a sodium fast reactor thermal stratification modeling case study, where we used a densely connected convolutional neural network to predict turbulent viscosity during the reactor transient with consideration of data noise. We benchmark its performance against several optimization approaches, including baseline deep ensemble, evolutionary algorithm-optimized ensemble, ensemble formed via random search combined with greedy selection, and a BO ensemble using random initialization. Here, our results demonstrate superior performance of the developed BODE approach. In noise-free scenarios, BODE notably reduces incorrect aleatoric uncertainty and significantly enhances predictive accuracy. Under conditions of 5% and 10% Gaussian noise, BODE adaptively quantifies uncertainty proportional to data noise, achieving up to an 80% reduction in root mean square error compared to baseline methods and producing well-calibrated prediction intervals.

Bayesian optimization

Chemoproteogenomic stratification of the missense variant cysteinome

Abstract Cancer genomes are rife with genetic variants; one key outcome of this variation is widespread gain-of-cysteine mutations. These acquired cysteines can be both driver mutations and sites targeted by precision therapies. However, despite their ubiquity, nearly all acquired cysteines remain unidentified via chemoproteomics; identification is a critical step to enable functional analysis, including assessment of potential druggability and susceptibility to oxidation. Here, we pair cysteine chemoproteomics—a technique that enables proteome-wide pinpointing of functional, redox sensitive, and potentially druggable residues—with genomics to reveal the hidden landscape of cysteine genetic variation. Our chemoproteogenomics platform integrates chemoproteomic, whole exome, and RNA-seq data, with a customized two-stage false discovery rate (FDR) error controlled proteomic search, which is further enhanced with a user-friendly FragPipe interface. Chemoproteogenomics analysis reveals that cysteine acquisition is a ubiquitous feature of both healthy and cancer genomes that is further elevated in the context of decreased DNA repair. Reference cysteines proximal to missense variants are also found to be pervasive, supporting heretofore untapped opportunities for variant-specific chemical probe development campaigns. As chemoproteogenomics is further distinguished by sample-matched combinatorial variant databases and is compatible with redox proteomics and small molecule screening, we expect widespread utility in guiding proteoform-specific biology and therapeutic discovery.

Desai, Heta (ORCID:0000000343621707)

Stratification of fluoride uptake among enamel crystals with age elucidated by atom probe tomography

Dental enamel is subjected to a lifetime of de- and re-mineralization cycles in the oral environment, the cumulative effects of which cause embrittlement with age. However, the understanding of atomic scale mechanisms of dental enamel aging is still at its infancy, particularly regarding where compositional differences occur in the hydroxyapatite nanocrystals and what underlying mechanisms might be responsible. Here, we use atom probe tomography to compare enamel from a young (22 years old) and a senior (56 years old) adult donor tooth. Findings reveal that the concentration of fluorine is elevated in the shells of senior nanocrystals relative to young, with less significant differences between the cores or intergranular phases. It is proposed that the embrittlement of enamel is driven, at least in part, by the infusion of fluorine into the nanocrystals and that the principal mechanism is de- and re-mineralization cycles that preferentially erode and rebuild the nanocrystals shells.

36 MATERIALS SCIENCE

Effect of seasonal anoxia on geochemical cycling in a stratified pond: Comparison to cooler pond conditions 40 years ago

Seasonal stratification in temperate lakes deeper than a few meters creates favorable conditions for pronounced vertical redox zones, often resulting in anaerobic hypolimnions and significant geochemical changes. Here, this study examined thermocline formation and trace element behavior in a seasonally stratified pond amid rising air temperatures. Over two years, data were collected from Pond B at the US Department of Energy Savannah River Site in Aiken, South Carolina. Pond B, a man-made monomictic reservoir, received cooling water from a nuclear reactor from 1961 to 1964. Strong thermal stratification forms a distinct thermocline in May and progresses downward until November. Compared to the 1980s, this study shows a delayed onset and extended duration of stratification. The prolonged summer stratification reduces deep water oxygen replenishment, extending hypoxic conditions. Trace and major elements sampled in the water column revealed strong correlations between As, Fe, and Mn profiles, with concentrations increasing by 1–2 orders of magnitude in the anaerobic hypolimnion. This period captured the seasonal transition from winter mixing to summer stratification to fall overturn. Under anoxic conditions, Fe(III) reduces to Fe(II) in the sediment, releasing dissolved iron into the water column. The extended anoxic periods likely promoted arsenic release from sediments. Prolonged anoxia may enhance arsenic mobilization and solubility in the lake. This study illustrates how climate-induced changes in seasonal stratification of contaminated waters can convert contaminant sinks into sources, offering insights into the cycling of arsenic and other dissolved ions in stratified lakes and their implications for water quality management.

Anoxic conditions

Sedimentation and shear-induced dynamics of spheroids in fluids with spatial viscosity variations

A generalized reciprocal theorem is used to relate the force and torque induced on a particle in an inertia-less fluid with small variation in viscosity to integrals involving Stokes flow fields and the spatial dependence of viscosity. These resistivity expressions are analytically evaluated using spheroidal harmonics and then used to obtain the mobility of the spheroid during sedimentation, and in linear flows, of a fluid with linear viscosity stratification. The coupling between the rotational and translational motion induced by stratification rotates the spheroid’s centerline, creating a variety of rotational and translational dynamics dependent upon the particle’s aspect ratio, κ, and the component of the stratification unit vector in the gravity direction, d g . Spheroids with 0.55 ⪅ κ ⪅ 2.0 exhibit the largest variety of settling behaviors. Interestingly, this range covers most microplastics and typical microorganisms. One of the modes include a stable orientation dependent only on κ and d g , but independent of initial orientation, thus allowing for the potential control of settling angles and sedimentation rates. In a simple shear flow, cross-streamline migration occurs due to the stratification-induced force generated on the particle. Similarly, a particle no longer stays at the stagnation point of a uniaxial extensional flow. While fully analytical results are obtained for spheroids, numerical simulations provide a source of validation. These simulations also provide additional insights into the stratification-induced force- and torque-producing mechanisms through the stratification-induced stress, which is not accessed in the reciprocal theorem-based analytical calculations.

Geophysical and Geological Flows: Stratified flows

Low-Level Liquid-Bearing Clouds Contribute to Seasonal Lower Atmosphere Stability and Surface Energy Forcing over a High-Mountain Watershed Environment

Measurements of atmospheric structure and surface energy budgets distributed along a high-altitude moun tain watershed environment near Crested Butte, Colorado, from two separate, but coordinated, field campaigns, Surface Atmosphere Integrated field Laboratory (SAIL) and Study of Precipitation, the Lower Atmosphere, and Surface for Hydrometeorology (SPLASH), are analyzed. This study identifies similarities and differences in how clouds influence the radiative budget over one snow-free summer season (2022) and two snow-covered seasons (2021/22; 2022/23) for this alpine location. A relationship between lower-tropospheric stability stratification and longwave radiative flux from the presence or absence of clouds is identified. When low clouds persisted, often with signatures of supercooled liquid in win ter, the lower troposphere experienced weaker stability, while radiatively clear skies that are less likely to be influenced by liquid droplets were associated with appreciably stronger lower-tropospheric stratification. Corresponding surface turbu lent heat fluxes partitioned differently based upon the cloud–stability stratification regime derived from early morning radiosounding profiles. Combined with the differences in the radiative budget largely resulting from dramatic seasonal dif ferences in surface albedo, the lower atmosphere stratification, surface energy budget, and near-surface thermodynamics are shown to be modified by the effective longwave radiative forcing of clouds. The diurnal evolution of thermodynamics and surface energy components varied depending on the early morning stratification state. Thus, the importance of quies cent versus synoptically active large-scale meteorology is hypothesized as a critical forcing for cloud properties and associ ated surface energy budget variations. The physical relationships between clouds, radiation, and stratification can provide a useful suite of metrics for process understanding and to evaluate numerical models in such an undersampled, highly com plex terrain environment.

54 ENVIRONMENTAL SCIENCES

Coherent structures in stably stratified wall-bounded turbulent flows

To date, a growing body of literature has documented the existence and impacts of coherent structures known as large- and very-large-scale motions within wall-bounded turbulent flows under neutral and unstable thermal stratification. These coherent structures can account for a considerable fraction of the overall turbulent transport and have been found to modulate small-scale turbulent fluctuations near the wall. In the context of stably stratified flows, however, the examination of such coherent structures has garnered relatively little attention. Stable stratification limits vertical transport and turbulent mixing within flows, which makes it unclear the extent to which previous findings on coherent structures under unstable and neutral stratification are applicable to stably stratified flows. In this study, we investigate the existence and characteristics of coherent structures under stable stratification with a wide range of statistical and spectral analyses. Outer peaks in premultiplied spectrograms under weak stability indicate the presence of large-scale motions, but these peaks become weaker and eventually vanish with increasing stability. Quadrant analysis of turbulent transport efficiencies (the ratio of net fluxes to their respective downgradient components) demonstrates dependencies on both stability and height above ground, which is evidence of morphological differences in the coherent structures under increasing stability. Amplitude modulation by large-scale streamwise velocity was found to decrease with increasing gradient Richardson number, whereas modulation by large-scale vertical velocity was approximately zero across all stability ranges. For sufficiently stable stratification, large eddies are suppressed enough to limit any inner–outer scale interactions.

Greene, Brian R. (ORCID:0000000343766818)

Expanded Understanding of the Western Antarctic Peninsula Sea‐Ice Environment Through Local and Regional Observations at Palmer Station

Abstract The Western Antarctic Peninsula (WAP) has been experiencing rapid regional warming since at least the 1950s, however, the impacts of this warming at the local scale are variable and nuanced. Previous studies that have linked sea‐ice variability to biogeochemical cycles and food web dynamics often combine local‐scale biogeochemical data with coarse‐resolution regional satellite sea‐ice data, which may not adequately capture local sea‐ice conditions. In this study, we analyzed local‐scale in situ sea‐ice observations collected as part of a 28‐year record (1992–2020) from the Palmer Long‐Term Ecological Research site at Anvers Island, mid‐WAP, in conjunction with isotopically‐derived sea‐ice meltwater (SIM) fractions and satellite‐derived sea‐ice motion and concentration, to quantify the variability and long‐term trends in local sea‐ice behavior. In situ sea ice observations at Palmer Station displayed higher variability than satellite observations and showed no significant declines over this time, despite region‐wide declines identified in prior studies. Higher spring SIM fractions were attributed to strong northward sea‐ice motion throughout the winter. Applying these local‐scale sea‐ice insights to similarly scaled stratification and chlorophyll‐ a measurements, we found that a longer‐lasting, more consistent sea‐ice pack led to greater water column stratification following the spring sea‐ice retreat. Greater sea‐ice persistence and stronger stratification led to larger peaks in chlorophyll‐ a , though sea‐ice metrics did not explain the positive temporal trends in either stratification strength or chlorophyll‐ a . Through this study, we identify how local sea‐ice observations and meltwater data can enhance satellite data to build an understanding of the intricate connections between ice, water column dynamics, and phytoplankton.

Goodell, E.

SAM Code Enhancements for Modeling of Liquid Metal-Cooled Fast Reactor Concepts

The SAM code is under development and supported by DOE-NE’s Nuclear Energy Advanced Modeling and Simulation program as a modern system-level modeling and simulation tool for advanced non-light water reactor safety analyses. These advanced reactor concepts incorporate novel and improved approaches to achieve safety and economic feasibility. This report summarizes two major efforts in addressing the modeling gaps in SAM for liquid-metal-cooled fast reactor (LMFR) applications, i.e. thermal mixing and stratification phenomena in large pools and corrosion-oxidation of components in flowing lead. A new one-dimensional model for thermal mixing and stratification effects in large pools and enclosures is developed and implemented. Thermal mixing and stratification occur when fluid enters a pool at a temperature different than the bulk fluid itself, a scenario often encountered during transients in pool-type systems. These phenomena are critical for the safety of reactors, impacting phenomena like natural circulation, which is essential for passive cooling. The improved model in SAM addresses limitations of state-of-the-art approaches by combining one-dimensional (1D) channels, representing the coolant jet flow, with lumped-parameter zero-dimensional (0D) pools, representing the rest of coolant in the tank. Energy exchange between the 1D jet and the 0D pools is based on heat transfer correlations calibrated against 3D simulations. It is verified that this model can handle various flow configurations, including hot jets in colder pools, cold jets in hotter pools, and the presence of features like ceilings, free surfaces, and obstacles. Additionally, validation against experimental data demonstrates the ability of the model to capture mixing and stratification effects in a wide range of conditions. The flexibility and improved accuracy of the new model make it a valuable tool for reactor safety analysis, allowing for the simulation of different geometries encountered in advanced reactors. A system-level corrosion modeling capability is developed and implemented in SAM to support Lead Fast Reactor (LFR) development. Although the initial focus of this capability will be on LFR application, this can later be expanded to include other liquid metals such as Lead-Bismuth Eutectic (LBE) and PbLi. This report summarizes the common corrosion mitigation strategies and outlines the progress on implementing and validating a corrosion-oxidation model in SAM. Verification and validation of the corrosion-oxidation portion of the model was performed using analytical solution and measured data from samples tested in the non-isothermal pumped lead loop at IPPE Obninsk. The iron transport and corrosion/precipitation portion of the model was assessed using an analytical model and measured corrosion depths from a natural convection lead loop experiment performed at CEA. It is demonstrated that the model implemented in SAM performed well in these assessments.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS

Numerical Simulation and Experimental Comparison of System Analysis Module 1D Mixing Model for Cold Shock Transients in the Gallium Thermal-Hydraulic Mixing Facility

Abstract Liquid metals are being investigated as coolants in many advanced reactor designs because of their high thermal conductivity and effectiveness at high temperatures. However, they often pose challenges to reactor operation and safety because of the complex thermal mixing and stratification in the plenum of pool-type reactor designs. The advanced system analysis code System Analysis Module (SAM) currently under development at Argonne National Laboratory aims to develop and implement thermal mixing models to accurately capture these complex thermal fluid behaviors. In this study, the SAM thermal mixing model was compared against experimental data from the Gallium Thermal-Hydraulic Experiment facility, a scaled liquid metal test facility that uses gallium as a surrogate fluid to investigate the stratification and thermal mixing of low-Prandtl-number fluids in the upper plenum of a liquid metal-cooled reactor. Two cold shock transient cases were used: one with stable stratified flow (Ri = 32) and one with stronger thermal mixing (Ri = 0.5). The resultant temperatures were then compared with the experimental temperatures over the entire plenum to assess the ability of the mixing models to capture the thermal behavior and to better correspond mixing parameters to various flow scenarios. Generally, the zero-dimensional mixing model was more capable of capturing the bulk temperature of the component modeled assuming that an accurate mass flow rate was provided, but it was inherently unable to capture thermal gradients in space. The one-dimensional mixing model was capable of capturing that the thermal gradients provided accurate selection of the mixing coefficients. Further, the temperature at the outlet junction was compared over time for each of the mixing models with the recorded experimental temperature. The implemented mixing models demonstrated the ability to effectively capture the overall thermal behavior for stronger mixing scenarios but struggled with more stably stratified flows. It was found that a system analysis code's covering of the entire range of different operating conditions still remains a challenging task, and it is suggested that further model and closure improvements are necessary to accurately capture complex thermal mixing and stratification phenomena.

stratification