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NASA NTRS1980

Lunar asymmetry and palaeomagnetism

A model is proposed for the early lunar evolution which accounts for the compositional asymmetry between the nearside and farside of the moon and the natural remanent magnetism of lunar rocks. According to the model, the preferred gravitational energy state consisted of an asymmetric accumulation of a liquid iron alloy (Fe-Ni and a small amount of sulfur) which displaces upwards the cold primordial undifferentiated core. The resulting depth asymmetry of the outer partially molten zone leads eventually to the subcrustal accumulation of light magnesium-rich pyroxenes and olivine, preferentially in one hemisphere, sufficient to explain the offset and also indirectly providing a possible explanation for the nearside concentration of KREEP and mass basalt. Slow downward migration of iron releases gravitational energy sufficient for convection and dynamo generation in an iron layer for about a billion years.

Stevenson, D. J.↗

DOE OSTI2023

Design of a prototypical natural circulation water-based reactor cavity cooling system (RCCS) for a pebble-bed generic FHR

A prototypical natural circulation water-based reactor cavity cooling system (RCCS) for the UC Berkeley Mark-1 pebble-bed gFHR is designed based on one-dimensional thermal hydraulics modeling and optimization implemented in an in-house MATLAB code. The model employs a lumped core consisting of fuel pebble and graphite pebble regions, while the graphite reflector, vessel, and RCCS are represented as separate but energy-coupled regions. The model is derived based on steady state energy balance equations accounting for conductive heat transfer from the lumped core to the vessel and subsequent radiative heat transfer to the RCCS and convective heat transfer in the water. Further, mass flow rate is calculated based on momentum and thermal energy balance in the RCCS. Starting with ANL’s water NSTF as baseline, effects of RCCS design parameters such as size of the plate between pipes, pipe diameter, source-to-sink distance, surface emissivity, and pitch from the core are examined in an integral effects framework which accounts for subsequent variation of the mass flow rate, number of pipes, convection coefficient, mean region and surface temperatures, radiative view factors, and water outlet temperature. The importance of including a prototypical reactor design in RCCS design calculations is emphasized as the calculations show that temperature drops from the core to the RCCS fluid to transfer the heat tend to be the limitation not the heat removal capacity of the fluid. A closed-loop design is obtained with capability to safely remove up to 0.72% of the nominal reactor power at maximum estimated peak conditions and 0.40% at shutdown. The design is based on physics calculations and does not account for economic optimization.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2021

X-ray Imaging-Based Void Fraction Measurement in Saturated Flow Boiling Experiments with Seawater Coolant

Recent studies have shown that the presence of dissolved salts in water can exhibit peculiar flow boiling and two-phase flow regimes. Two-phase flow and convective flow boiling are typically characterized with the help of void fraction measurements. To quantitatively improve our understanding of two-phase flow and boiling phenomenon with seawater coolant, void fraction data are needed, which can not be obtained from optical imaging. In this paper, we present experimental void fraction measurements of saturated flow boiling of tap water and seawater using X-ray radiography. X-rays with a maximum energy level of 40 KeV were used for imaging the exit region of the heated test section. At lower heat flux levels, the two phase flow in seawater was bubbly and homogeneous in nature, resulting in higher void fractions as compared to tap water. With an increase in heat flux, the flow regime was similar to slug flow, and void fraction measurements approached similarity with tap water. The predicted pressure drop using the measured void faction shows good agreement with the measured total pressure drop across the test section, demonstrating the validity of the measurement process.

Eckels, Seth↗

NASA NTRS1994

Nonequilibrium radiation and chemistry models for aerocapture vehicle flowfields

The primary accomplishments of the project were as follows: (1) From an overall standpoint, the primary accomplishment of this research was the development of a complete gasdynamic-radiatively coupled nonequilibrium viscous shock layer solution method for axisymmetric blunt bodies. This method can be used for rapid engineering modeling of nonequilibrium re-entry flowfields over a wide range of conditions. (2) Another significant accomplishment was the development of an air radiation model that included local thermodynamic nonequilibrium (LTNE) phenomena. (3) As part of this research, three electron-electronic energy models were developed. The first was a quasi-equilibrium electron (QEE) model which determined an effective free electron temperature and assumed that the electronic states were in equilibrium with the free electrons. The second was a quasi-equilibrium electron-electronic (QEEE) model which computed an effective electron-electronic temperature. The third model was a full electron-electronic (FEE) differential equation model which included convective, collisional, viscous, conductive, vibrational coupling, and chemical effects on electron-electronic energy. (4) Since vibration-dissociation coupling phenomena as well as vibrational thermal nonequilibrium phenomena are important in the nonequilibrium zone behind a shock front, a vibrational energy and vibration-dissociation coupling model was developed and included in the flowfield model. This model was a modified coupled vibrational dissociation vibrational (MCVDV) model and also included electron-vibrational coupling. (5) Another accomplishment of the project was the usage of the developed models to investigate radiative heating. (6) A multi-component diffusion model which properly models the multi-component nature of diffusion in complex gas mixtures such as air, was developed and incorporated into the blunt body model. (7) A model was developed to predict the magnitude and characteristics of the shock wave precursor ahead of vehicles entering the Earth's atmosphere. (8) Since considerable data exists for radiating nonequilibrium flow behind normal shock waves, a normal shock wave version of the blunt body code was developed. (9) By comparing predictions from the models and codes with available normal shock data and the flight data of Fire II, it is believed that the developed flowfield and nonequilibrium radiation models have been essentially validated for engineering applications.

Carlson, Leland A.↗

NASA NTRS2001

Use of a Data-Linked Weather Information Display and Effects on Pilot Navigation Decision Making in a Piloted Simulation Study

This study provides recommendations to the FAA and to prospective manufacturers based on an exploration of the effects of data link weather displays upon pilot decision performance. An experiment was conducted with twenty-four current instrument rated pilots who were divided into two equal groups and presented with a challenging but realistic flight scenario involving weather containing significant embedded convective activity. All flights were flown in a full-mission simulation facility within instrument meteorological conditions. The inflight weather display depicted NexRad images, graphical METARs and textual METARs. The objective was to investigate the potential for misuse of a weather display, and incorporate recommendations for the design and use of these displays. The primary conclusion of the study found that the inflight weather display did not improve weather avoidance decision making. Some of the reasons to support this finding include: the pilot's inability to easily perceive their proximity to the storms, increased workload and difficulty in deciphering METAR textual data. The compelling nature of a graphical weather display caused many pilots to reduce their reliance on corroborating weather information from other sources. Minor changes to the weather display could improve the ability of a pilot to make better decisions on hazard avoidance.

Yuchnovicz, Daniel E.↗

NASA NTRS2003

Two-Dimensional Transport Studies for the Composition and Structure of the Io Plasma Torus

The overall objective of this project is to investigate the roles of local and spatially extended plasma sources created by Io, plasma torus chemistry, and plasma convective and diffusive transport in producing the long-lived S(+), S(++) and O(+) radial ribbon structures of the plasma torus, their System III longitude and local-time asymmetries, their energy sources and their possible time variability. To accomplish this objective, two-dimensional [radial (L) and System III longitude] plasma transport equations for the flux-tube plasma content and energy content will be solved that include the convective motions for both the east-west electric field and co-rotational velocity-lag profile near Io s orbit, radial diffusion, and the spacetime dependent flux-tube production and loss created by both neutral-plasma and plasma-ion reaction chemistry in the plasma torus. For neutral-plasma chemistry, the project will for the first time undertake the calculation of realistic three-dimensional, spatially-extended, and time-varying contributions to the flux-tube ion-production and loss that are produced by Io's corona and extended neutral clouds. The unknown two-dimensional spatial nature of diffusion in the plasma transport will be isolated and better defined in the investigation by the collective consideration of the foregoing different physical processes. For energy transport, the energy flow from hot pickup ions (and a new electron source) to thermal ions and electrons will be included in investigating the System III longitude and local-time temperature asymmetries in the plasma torus. The research is central to the scope of the NASA Sun-Earth Connection Roadmap in Quest II Campaign 4 "Comparative Planetary Space Environments" by addressing key questions for understanding the magnetosphere of planets with high rotation rates and large internal plasma sources and, in addition, is of considerable importance to the NASA Solar System Exploration Science Theme. In this regard, Jupiter is the most extreme example with its rapid rotation and with its inner Galilean satellite Io providing the dominant plasma source for the magnetosphere.

Smyth, William H.↗

NASA NTRS2010

Comparisons of Supergranule Properties from SDO/HMI with Other Datasets

While supergranules, a component of solar convection, have been well studied through the use of Dopplergrams, other datasets also exhibit these features. Quiet Sun magnetograms show local magnetic field elements distributed around the boundaries of supergranule cells, notably clustering at the common apex points of adjacent cells, while more solid cellular features are seen near active regions. Ca II K images are notable for exhibiting the chromospheric network representing a cellular distribution of local magnetic field lines across the solar disk that coincides with supergranulation boundaries. Measurements at 304 A further above the solar surface also show a similar pattern to the chromospheric network, but the boundaries are more nebulous in nature. While previous observations of these different solar features were obtained with a variety of instruments, SDO provides a single platform, from which the relevant data products at a high cadence and high-definition image quality are delivered. The images may also be cross-referenced due to their coincidental time of observation. We present images of these different solar features from HMI & AIA and use them to make composite images of supergranules at different atmospheric layers in which they manifest. We also compare each data product to equivalent data from previous observations, for example HMI magnetograms with those from MDI.

Pesnell, William Dean↗

NASA NTRS1991

Numerical simulations of turbulent thermal convection with differential rotation

The solar nebula, from which the planets in our solar system formed, featured a disk of gas and dust grains in rapid, differential rotation, and at some stage was likely to have been unstable to thermal convection. This situation is suspected by many to lead to significant turbulent Reynolds stress production and angular momentum transport in such systems, and estimates of transport rates have been attempted from unsubstantiated phenomenological models. In order to determine the circumstances and physical conditions under which our own planetary system formed and to explain recent observations of young stellar systems, it is necessary to develop realistic models of heat and angular momentum transport for such flows. Developing an understanding of complicated flows featuring thermal convection, rotation, and shear is also of wide interest in stellar astrophysics and in planetary and terrestrial atmospheric studies. The ultimate objective is to develop workable models based on the numerical simulations for constructing global solar nebula models; viz., relatively simple prescriptions for heat and angular momentum fluxes from given system parameters (e.g., ratios of rotation, shear, and convective lapse rates) are characterized, quantified, and developed. Toward this end, our program has been to attempt to understand the behavior of the direct numerical simulations of Boussinesq convection, which, despite the complexity of the results, is still an overly simplified approximation to the real system and should be more amenable to analysis. These results are also intended to be tested against turbulence models, especially those designed for atmospheric boundary layers, and may provide a basis for subgrid-scale models. In order to make the numerical simulations more realistic with regard to the solar nebula problem, a fully compressible code that will allow incorporation of large density stratifications and realistic thermodynamic and radiative properties is developed. In order to explore the properties of these flows at the very high values of Re found in natural systems and the very low values of Pr found in most astrophysical contexts, we will need to employ large-eddy simulations for which we want to determine the most appropriate subgrid-scale model to incorporate.

Cabot, William H.↗

NASA NTRS2005

Potassium-bearing Iron-Nickel Sulfides in Nature and High-Pressure Experiments: Geochemical Consequences of Potassium in the Earth's Core

Introduction: Potassium (K) as a large ion lithophile element has dominantly been concentrated in the Earth s crust and the mantle through differentiation, and in the form of K-40 contributes to the planet s heat budget. However, whether or not K also enters core-forming phases, has been debated for over three decades. Arguments favoring entry of K in the core are based on: (1) K-sulfide (with Fe, Ni, Cu, Na, and Cl; djerfisherite) found in highly reduced enstatite chondrites (or aubrites, enstatite achondrites); (2) demonstration that K, owing to an s-d electronic switch at high-pressure, exhibits transition- element like character, (3) solubility of measurable K in Fe-Ni-S liquids at high pressure, temperature conditions, and (4) models of cooling of the core that seem to require, besides convection, some form of radioactivity, and thus lending support to the experimental work. In this contribution, we assess the effect of sequestering K in the core, as it is perhaps an element that is a key to reconciling geochemistry, paleomagnetism, accretion, and thermal evolution models for the planet.

Keshav, S.↗

NASA NTRS2014

Extreme Thunderstorms as Seen by Satellite

Extreme events by their nature fall outside the bounds of routine experience. With imperfect or ambiguous measuring systems, it is appropriate to question whether an unusual measurement represents an extreme event or is the result of instrument errors or other sources of noise. About three weeks after the Tropical Rainfall Measuring Mission (TRMM) satellite began collecting data in Dec 1997, a thunderstorm was observed over northern Argentina with 85 GHz brightness temperatures below 50 K and 37 GHz brightness temperatures below 70 K (Zipser et al. 2006). These values are well below what had previously been observed from satellite sensors with lower resolution. The 37 GHz brightness temperatures are also well below those measured by TRMM for any other storm in the subsequent 16 years. Without corroborating evidence, it would be natural to suspect a problem with the instrument, or perhaps an irregularity with the platform during the first weeks of the satellite mission. But the TRMM satellite also carries a radar and a lightning sensor, both confirming the presence of an intense thunderstorm. The radar recorded 40+ dBZ (decibels relative to Z) reflectivity up to about 19 km altitude. More than 200 lightning flashes per minute were recorded. That same storm's 19 GHz brightness temperatures below 150 K would normally be interpreted as the result of a low-emissivity water surface (e.g., a lake, or flood waters) if not for the simultaneous measurements of such intense convection. This paper will examine records from TRMM and related satellite sensors including SSMI and AMSR-E to find the strongest signatures resulting from thunderstorms, and distinguishing those from sources of noise. The lowest brightness temperatures resulting from thunderstorms as seen by TRMM have been in Argentina in November and December. For SSMI sensors carried on five DMSP satellites examined so far, the lowest thunderstorm-related brightness temperatures have been from Argentina in November - December and from Minnesota in June-July. The Minnesota cases were associated with spotter reports of large hail, significant severe wind, and tornadoes. Those locations have the record holders for each satellite. This paper will show examples of cases with the lowest brightness temperatures, and map the locations of these and other storms with brightness temperatures nearly as low. Higher resolution data from the field program MC3E and possibly from IPHEX will be considered for context.

Cecil, Daniel J.↗

NASA NTRS2023

Salt Distribution from Freezing Intrusions in Ice Shells on Ocean Worlds: Application to Europa

Several icy moons and dwarf planets appear to have hosted subsurface liquid water. Liquid water intruding upwards into the icy outer shells of these worlds freezes, forming ice and (from ocean solutes) non-ice solids. Here, we model concentrated aqueous solutions below 273 K to simulate the compositional evolution of freezing spherical intrusions. Starting solutions are based on five previously reported compositional end members for Europa's ocean. For moderate-pH end members dominated by chloride, sulfate, and/or carbonate, the solids formed include Ca-, Mg-, and Na-sulfates and -carbonates, as well as Na- and K-chlorides. For silica-rich, high-pH end members, abundant amorphous silica forms with, potentially, similarly abundant NaOH and KOH. We further develop a new numerical model to compute the spatial distribution of the formed solids and residual brine as freezing progresses. If non-ice solids settle to the bottom, their deposits tend to have stacked hourglass shapes, widening each time the crystallization temperature of a new solid is reached. We discuss the applicability of this model to vertical fractures and global freezing of a subsurface ocean. These results inform (i) how compositional heterogeneities may affect the thermophysical properties of ice shells, which in turn influence convective and cryovolcanic transport, (ii) the compatibility of brine pockets with physicochemical conditions suitable for microbial life, and (iii) possible measurements of compositional heterogeneities within ice shells by spacecraft such as NASA's Europa Clipper and ESA's JUICE missions. The methodology developed here is applicable to other ice-covered ocean worlds.

Planetary structure↗

DOE OSTI2024

Increased Occurrence of Large–Scale Windthrows Across the Amazon Basin

Convective storms with strong downdrafts create windthrows: snapped and uprooted trees that locally alter the structure, composition, and carbon balance of forests. Comparing Landsat imagery from subsequent years, we documented temporal and spatial variation in the occurrence of large (≥30 ha) windthrows across the Amazon basin from 1985 to 2020. Over 33 individual years, we detected 3179 large windthrows. Windthrow density was greatest in the central and western Amazon regions, with ~33% of all events occurring in ~3% of the monitored area. Return intervals for large windthrows in the same location of these “hotspot” regions are centuries to millennia, while over the rest of the Amazon they are >10,000 years. Our data demonstrate a nearly 4–fold increase in windthrow number and affected area between 1985 (78 windthrows and 6,900 ha) and 2020 (264 events and 32,170 ha), with more events of >500 ha size since 1990. Such extremely large events (>500 ha up to 2,543 ha) are responsible for interannual variation in the overall median (84 ± 5.2 ha; ±95% CI) and mean (147 ± 13 ha) windthrow area, but we did not find significant temporal trends in the size distribution of windthrows with time. Our results document increased damage from convective storms over the past 40 years in the Amazon, filling a gap in temporal records for tropical regions. Our publicly accessible large windthrow database provides a valuable tool for exploring dynamic conditions leading to damaging storms and their ecological impact on Amazon forests.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1975

Pressure- and buoyancy-driven thermal convection in a rectangular enclosure

Results are presented for unsteady laminar thermal convection in compressible fluids at various reduced levels of gravity in a rectangular enclosure which is heated on one side and cooled on the opposite side. The results were obtained by solving numerically the equations of conservation for a viscous, compressible, heat-conducting, ideal gas in the presence of a gravitational body force. The formulation differs from the Boussinesq simplification in that the effects of variable density are completely retained. A conservative, explicit, time-dependent, finite-difference technique was used and good agreement was found for the limited cases where direct comparison with previous investigations was possible. The solutions show that the thermally induced motion is acoustic in nature at low levels of gravity and that the unsteady-state rate of heat transfer is thereby greatly enhanced relative to pure conduction. The nonlinear variable density profile skews the streamlines towards the cooler walls but is shown to have little effect on the steady-state isotherms.

Spradley, L. W.↗

NASA NTRS1995

Rheological transition in mantle convection with a composite temperature-dependent, non-Newtonian and Newtonian rheology

Numerical simulations of mantle convection with a composite temperature-dependent, Newtonian and non-Newtonian creep law have revealed a transition in the dominant creep mechanism with the increasing vigour of convection. Newtonian creep is found to dominate in the low Rayleigh number regime. With sufficiently high effective Rayleigh number, the overall creep mechanism in the convective flow becomes non-Newtonian. The transitional Rayleigh number increases strongly with the activation energy. These results would suggest a scenario that in the early epochs of Earth the flow in the mantle would have been governed by non-Newtonian rheology and would have exhibited both strong spatial and temporal fluctuations. With time the flow mechanism would behave like a Newtonian fluid and would have a different time-dependent character. In time-dependent Newtonian-dominated flows there are still localized features with distinctly non-Newtonian character. Our analysis of the relative contributions to the lateral viscosity field supports the idea that the inference of the nature of lateral viscosity heterogeneities by seismic tomography may be strongly contaminated by the dominant non-Newtonian contributions to the total lateral viscosity field.

Van Den Berg, Arie P.↗

NASA NTRS2005

Mineral Composition and Abundance of the Rocks and Soils at Gusev and Meridiani from the Mars Exploration Rover Mini-TES Instruments

The Miniature Thermal Emission Spectrometer (Mini-TES) has provided remote measurements of mineralogy, thermophysical properties, and atmospheric temperature profile and composition of the outcrops, rocks, spherules, and soils surrounding the Spirit and Opportunity Rovers. The mineralogy of volcanic rocks provides insights into the composition of the source regions and the nature of martian igneous processes. Carbonates, sulfates, evaporites, and oxides provide information on the role of water in the surface evolution. Oxides, such as crystalline hematite, provide insight into aqueous weathering processes, as would the occurrence of clay minerals and other weathering products. Diurnal temperature measurements can be used to determine particle size and search for the effects of sub-surface layering, which in turn provide clues to the origin of surficial materials through rock disintegration, aeolian transport, atmospheric fallout, or induration. In addition to studying the surface properties, Mini-TES spectra have also been used to determine the temperature profile in the lower boundary layer, providing evidence for convective activity, and have determined the seasonal trends in atmospheric temperature and dust and cloud opacity.

Christensen, P. R.↗

NASA NTRS2012

Comparison of Controller and Flight Deck Algorithm Performance During Interval Management with Dynamic Arrival Trees (STARS)

Managing the interval between arrival aircraft is a major part of the en route and TRACON controller s job. In an effort to reduce controller workload and low altitude vectoring, algorithms have been developed to allow pilots to take responsibility for, achieve and maintain proper spacing. Additionally, algorithms have been developed to create dynamic weather-free arrival routes in the presence of convective weather. In a recent study we examined an algorithm to handle dynamic re-routing in the presence of convective weather and two distinct spacing algorithms. The spacing algorithms originated from different core algorithms; both were enhanced with trajectory intent data for the study. These two algorithms were used simultaneously in a human-in-the-loop (HITL) simulation where pilots performed weather-impacted arrival operations into Louisville International Airport while also performing interval management (IM) on some trials. The controllers retained responsibility for separation and for managing the en route airspace and some trials managing IM. The goal was a stress test of dynamic arrival algorithms with ground and airborne spacing concepts. The flight deck spacing algorithms or controller managed spacing not only had to be robust to the dynamic nature of aircraft re-routing around weather but also had to be compatible with two alternative algorithms for achieving the spacing goal. Flight deck interval management spacing in this simulation provided a clear reduction in controller workload relative to when controllers were responsible for spacing the aircraft. At the same time, spacing was much less variable with the flight deck automated spacing. Even though the approaches taken by the two spacing algorithms to achieve the interval management goals were slightly different they seem to be simpatico in achieving the interval management goal of 130 sec by the TRACON boundary.

Battiste, Vernol↗

NASA NTRS1983

Three-Dimensional Tracer Model Study of Atmospheric CO2 - Response to Seasonal Exchanges with the Terrestrial Biosphere

A three-dimensional tracer transport model is used to investigate the annual cycle of atmospheric CO2 concentration produced by seasonal exchanges with the terrestrial biosphere. The tracer model uses winds generated by a global general circulation model to advect and convect CO2; no explicit diffusion coefficients are employed. A biospheric exchange function constructed from a map of net primary productivity, and Azevedo's (1982) seasonality of CO2 uptake and release closely simulates the annual cycles at coastal stations. The results show that zonal homogeneity in surface CO2 concentrations can never be achieved at mid-latitudes where the time scale for zonal mixing is longer than the time scale for biospheric exchange. Analysis of the zonal mean balance in the lower troposphere reveals that atmospheric transport processes may alter the CO2 response to local biospheric exchanges by 50% or more. Hence year-to-year variation of the annual CO2 cycle may result from the natural variability of the atmospheric circulation as well as from changes in the sources and sinks.

Fung, I.↗

NASA NTRS2000

Computations of Boiling in Microgravity

The absence (or reduction) of gravity, can lead to major changes in boiling heat transfer. On Earth, convection has a major effect on the heat distribution ahead of an evaporation front, and buoyancy determines the motion of the growing bubbles. In microgravity, convection and buoyancy are absent or greatly reduced and the dynamics of the growing vapor bubbles can change in a fundamental way. In particular, the lack of redistribution of heat can lead to a large superheat and explosive growth of bubbles once they form. While considerable efforts have been devoted to examining boiling experimentally, including the effect of microgravity, theoretical and computational work have been limited. Here, the growth of boiling bubbles is studied by direct numerical simulations where the flow field is fully resolved and the effects of inertia, viscosity, surface deformation, heat conduction and convection, as well as the phase change, are fully accounted for. Boiling involves both fluid flow and heat transfer and thus requires the solution of the Navier-Stokes and the energy equations. The numerical method is based on writing one set of governing transport equations which is valid in both the liquid and vapor phases. This local, single-field formulation incorporates the effect of the interface in the governing equations as source terms acting only at the interface. These sources account for surface tension and latent heat in the equations for conservation of momentum and energy as well as mass transfer across the interface due to phase change. The single-field formulation naturally incorporates the correct mass, momentum and energy balances across the interface. Integration of the conservation equations across the interface directly yields the jump conditions derived in the local instant formulation for two-phase systems. In the numerical implementation, the conservation equations for the whole computational domain (both vapor and liquid) are solved using a stationary grid and the phase boundary is followed by a moving unstructured two-dimensional grid. While two-dimensional simulations have been used for preliminary studies and to examine the resolution requirement, the focus is on fully three-dimensional simulations. The numerical methodology, including the parallelization and grid refinement strategy is discussed, and preliminary results shown. For buoyancy driven flow, the heat transfer is in good agreement with experimental correlations. The changes when gravity is turned off and/or fluid shear is added are discussed, as well as the difference between simulations of a layer freely releasing bubbles versus simulations using only one wavelength initial perturbation. Figure 1 shows the early stages of the formation of a three-dimensional bubble from a thin vapor layer. The boundary conditions are periodic in the x and y direction, the bottom is a hot and the top allows a free outflow. The jagged edge of the surface close to the bottom of the computational domain is due to some of the surface elements being on the other side of the domain and some elements not plotted by our plotting routine. In the second figure, we show the temperature distribution through two perpendicular planes.

Tryggvason, G.↗