Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “temperature gradient”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 415 records · Page 23

Progress in understanding the enhanced pedestal H-mode in NSTX

The paper describes the enhanced pedestal (EP) H-mode observed in the National Spherical Torus Experiment (NSTX). The defining characteristics of EP H-mode are given, namely i)transition after the L- to H-mode transition, ii) region of very steep ion temperature gradient, and iii) associated region of strong rotational shear. A newly observed long-pulse EP H-mode example shows quiescent behavior for as long as the heating and current drive sources are maintained. Cases are shown where the region of steep ion temperature gradient is located at the very edge, and cases where it is shifted up to 10 cm inward from the plasma edge; these cases are united by a common dependence of the ion temperature gradient on the toroidal rotation frequency shear. EP H-mode examples have been observed across a wide range of q95 and pedestal collisionality. No strong changes in the fluctuation amplitudes have been observed following the eP H-mode transition, and transport analysis indicates that the ion t hermal transport is comparable to or less than anticipated from a simple neoclassical transport model. Cases are shown where EP H-modes were reliably generated, through these low-q95 examples were difficult to sustain. A case where an externally triggered ELM precipitates the transition to EP H-mode is also shown, though an initial experiment designed to trigger EP-H-modes in this fashion was successful.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Progress In Understanding The Enhanced Petestal H-mode In NSTX

This paper describes the enhanced pedestal (EP) H-mode observed in the National Spherical Torus Experiment (NSTX). The defining characteristics of EP H-mode are given, namely i) transition after the L- to H-mode transition, ii) region of very steep ion temperature gradient, and iii) associated region of strong rotational shear. A newly observed long-pulse EP H-mode example shows quiescent behavior for as long as the heating and current drive sources are maintained. Cases are shown where the region of steep ion temperature gradient is located at the very edge, and cases where it is shifted up to 10 cm inward from the plasma edge; these cases are united by a common dependence of the ion temperature gradient on the toroidal rotation frequency shear. EP H-mode examples have been observed across a wide range of q 95 and pedestal collisionality. No strong changes in the fluctuation amplitudes have been observed following the eP H-mode transition, and transport analysis indicates that the ion thermal transport is comparable to or less than anticipated from a simple neoclassical transport model. Cases are shown where EP H-modes were reliably generated, through these low-q 95 examples were difficult to sustain. A case where an externally triggered ELM precipitates the transition to EP H-mode is also shown, though an initial experiment designed to trigger EP-H-modes in this fashion was successful.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

FINGERING CONVECTION AND CLOUDLESS MODELS FOR COOL BROWN DWARF ATMOSPHERES

This work aims to improve the current understanding of the atmospheres of brown dwarfs, especially cold ones with spectral types T and Y, whose modeling is a current challenge. Silicate and iron clouds are believed to disappear at the photosphere at the L/T transition, but cloudless models fail to reproduce correctly the spectra of T dwarfs, advocating for the addition of more physics, e.g., other types of clouds or internal energy transport mechanisms. We use a one-dimensional radiative/convective equilibrium code ATMO to investigate this issue. This code includes both equilibrium and out-of-equilibrium chemistry and solves consistently the PT structure. Included opacity sources are H{sub 2}-H{sub 2}, H{sub 2}-He, H{sub 2}O, CO, CO{sub 2}, CH{sub 4}, NH{sub 3}, K, Na, and TiO, VO if they are present in the atmosphere. We show that the spectra of Y dwarfs can be accurately reproduced with a cloudless model if vertical mixing and NH{sub 3} quenching are taken into account. T dwarf spectra still have some reddening in, e.g., J–H, compared to cloudless models. This reddening can be reproduced by slightly reducing the temperature gradient in the atmosphere. We propose that this reduction of the stabilizing temperature gradient in these layers, leading to cooler structures, is due to the onset of fingering convection, triggered by the destabilizing impact of condensation of very thin dust.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High spatial resolution temperature profile measurements of solid-oxide fuel cells

Temperature gradients resulting from local electrochemical reactions, current distribution and geometry of gas flow channels in solid oxide fuel cells (SOFCs) create thermal stresses, localized thermophysical property gradients and uneven property evolution, contributing to SOFC degradation. This paper presents a new method to perform temperature measurements (up to 800°C) at high spatial resolutions to monitor the operation of SOFCs. Using femtosecond laser irradiation, distributed fiber sensors were hardened for high temperature environment applications. Distributed fiber sensors were embedded in interconnected plates using an additive manufacturing method to perform temperature measurements with 4-mm spatial resolution during the operation of a planar fuel cell. The measurement revealed the impact of various H 2 fuel concentrations and current loads have on temperature profiles of the SOFC tested. Temperature variation on the anode side was found to be less than 5°C, and 3°C on the cathode side. The measurements were compared to results from a multiphysics fuel cell performance model simulating similar conditions. These simulations predicted similar temperature gradients, indicating the experimental data obtained is reasonable. The model also predicts that the effect of the embedded sensor has on the local temperature will be minimal and that the gradient of temperature in the gas channels will be captured despite the separation between the sensor and the gas flow. Finally, the high spatial resolution data harnessed by these distributed fiber sensors provides experimental support for model-based design and optimization to improve the operational efficiency and longevity of solid oxide fuel cells and fuel cell assemblies.

25 ENERGY STORAGE↗

Understanding Irrigation Impacts on Low-Level Jets over the Great Plains

Low-level jets (LLJs) over the Great Plains are well-known for their importance in transporting moisture from the Gulf of Mexico and forming precipitation in the Central US. However, the impact of irrigation practice on LLJs is rarely studied. To understand the irrigation impact on the Great Plains LLJs, the Weather Research and Forecasting (WRF) model is employed with and without an irrigation scheme. The simulated wind field is evaluated against the observed wind from Midlatitude Continental Convective Clouds Experiment (MC3E). The results show that adding irrigation improves the simulated wind, especially at lower altitudes below 800 hPa. Irrigation reduces the LLJ frequency over the Great Plains, mainly by reducing the intense LLJ frequency. The reduced LLJ frequency is caused by the irrigation-induced weakening of meridional wind. The favorable conditions for LLJs have been identified by examining the mechanism associated with LLJs: a ridge-like pattern with weak and calm synoptic-scale conditions in the mid-levels and a strong west-east temperature gradient at lower levels that promote meridional winds. Irrigation-induced cooling leads to a baroclinic pattern with high pressure at lower altitudes over the irrigation region and low pressure in the mid- and upper levels in the downstream region, resulting in a northerly component that hinders the formation of LLJs. Low-level surface cooling also decreases the west-east temperature gradient and hence weakens the thermal wind forcing. The irrigation-induced mid-level low and weaker west-east temperature gradient are responsible for the reduced meridional winds and the reduced LLJ frequencies.

Yang, Zhao↗

Geometric origin of the intrinsic transverse spin transport in a canted-antiferromagnet/heavy-metal heterostructure

We theoretically study the conditions under which an intrinsic spin Nernst effect–a transverse spin current induced by an applied temperature gradient–can occur in a canted-antiferromagnet insulator, such as LaFeO 3 and other materials of the same family. The spin Nernst effect may provide a microscopic mechanism for an experimentally observed anomalous thermovoltage in LaFeO 3 /Pt heterostructures, where spin is transferred across the insulator/metal interface when a temperature gradient is applied to LaFeO 3 parallel to the interface. We find that LaFeO 3 exhibits an intrinsic spin Nernst effect when inversion symmetry is broken on the axes parallel to both the applied temperature gradient and the direction of spin transport, which can result in a spin injection across the insulator/metal interface. Furthermore, our paper provides a general derivation of a symmetry-breaking-induced spin Nernst effect, which may open a path to engineering a finite spin Nernst effect in systems where it would otherwise not arise.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Global and Zonal-Mean Hydrological Response to Early Eocene Warmth

Earth's hydrological cycle is expected to intensify in response to global warming, with a “wet-gets-wetter, dry-gets-drier” response anticipated over the ocean. Subtropical regions (∼15°–30°N/S) are predicted to become drier, yet proxy evidence from past warm climates suggests these regions may be characterized by wetter conditions. Here we use an integrated data-modeling approach to reconstruct global and zonal-mean rainfall patterns during the early Eocene (∼56–48 million years ago). The Deep-Time Model Intercomparison Project (DeepMIP) model ensemble indicates that the mid- (30°–60°N/S) and high-latitudes (>60°N/S) are characterized by a thermodynamically dominated hydrological response to warming and overall wetter conditions. The tropical band (0°–15°N/S) is also characterized by wetter conditions, with several DeepMIP models simulating narrowing of the Inter-Tropical Convergence Zone. However, the latter is not evident from the proxy data. The subtropics are characterized by negative precipitation-evaporation anomalies (i.e., drier conditions) in the DeepMIP models, but there is surprisingly large inter-model variability in mean annual precipitation (MAP). Intriguingly, we find that models with weaker meridional temperature gradients (e.g., CESM, GFDL) are characterized by a reduction in subtropical moisture divergence, leading to an increase in MAP. These model simulations agree more closely with our new proxy-derived precipitation reconstructions and other key climate metrics and imply that the early Eocene was characterized by reduced subtropical moisture divergence. If the meridional temperature gradient was even weaker than suggested by those DeepMIP models, circulation-induced changes may have outcompeted thermodynamic changes, leading to wetter subtropics. This highlights the importance of accurately reconstructing zonal temperature gradients when reconstructing past rainfall patterns.

Margot J. Cramwinckel↗

Characteristics of Bay of Bengal Monsoon Depressions in the 21st Century

The controversy surrounding the observed trends in the frequency of South Asian Monsoon Depressions (MDs)1-4, the association of MDs with the summer season extremes5,6, and a moisture driven future precipitation response in Global Climate Models (GCMs)7,8 have elevated the importance of understanding climate change impacts on the characteristics of MDs. GCMs exhibit a significant relationship between the long-term mean occurrences of MDs and the strength of the background upper (lower) tropospheric meridional (zonal) winds and atmospheric moisture in the core genesis region of MDs. Likewise, the strength of the meridional tropospheric temperature gradient (MTG) in GCMs determines the trajectories of MDs over land. While monsoon dynamics progressively weakens in the future period, atmospheric moisture exhibits a strong increase, limiting the impact of changes in background dynamics on the frequency of MDs. Moreover, the weakening of the future MTG is many times weaker than its inherent underestimation in the GCMs. Hence the 21st century increase in radiative forcing does not significantly reduce the frequency of MDs or impact their trajectories over land in the GCMs. Although more wet extremes are expected to occur during the MD lifecycle, non-depression day extremes dominate the overall increase in extreme precipitation, which may render the monsoon extremes less predictable in the future.

Rastogi, Deeksha↗

Reducing Subjectivity in Geothermal Exploration Decision Making (Presentation); NREL(National Renewable Energy Laboratory)

Geothermal exploration projects have a significant amount of risk associated with uncertainties encountered in the discovery of the geothermal resource. Two of the largest challenges for increased geothermal deployment are 1) understanding when and how to proceed in an exploration program, and 2) when to walk away from a site. Current methodologies for exploration decision-making are formulatedby subjective expert opinion which can be incorrectly biased by expertise (e.g. geochemistry, geophysics), geographic location of focus, and the assumed conceptual model. The aim of this project is to develop a methodology for more objective geothermal exploration decision making at a given location, including go/no-go decision points to help developers and investors decide when to give up on alocation. In this scope, two different approaches are investigated: 1) value of information analysis (VOIA) which is used for evaluating and quantifying the value of a data before they are purchased, and 2) enthalpy-based exploration targeting based on reservoir size, temperature gradient estimates, and internal rate of return (IRR). The first approach, VOIA, aims to identify the value of aparticular data when making decisions with an uncertain outcome. This approach targets the pre-drilling phase of exploration. These estimated VOIs are highly affected by the size of the project and still have a high degree of subjectivity in assignment of probabilities. The second approach, exploration targeting, is focused on decision making during the drilling phase. It starts with a basicgeothermal project definition that includes target and minimum required production capacity and initial budgeting for exploration phases. Then, it uses average temperature gradient, reservoir temperature estimates, and production capacity to define targets and go/no-go limits. The decision analysis in this approach is based on achieving a minimum IRR at each phase of the project. This secondapproach was determined to be less subjective, since numerical inputs come from the collected data. And it helps to facilitate communication between project managers and exploration geologists in making objective go/no-go decisions throughout the different project phases.

15 GEOTHERMAL ENERGY↗

Assessment of New Approaches in Geothermal Exploration Decision Making: Preprint

Geothermal exploration projects have significant amount of risk associated with uncertainties encountered in the discovery of the geothermal resource. Understanding when and how to proceed in an exploration program, and when to walk away from a site, are two of the largest challenges for increased geothermal deployment. Current methodologies for exploration decision making is left to subjective by subjective expert opinion which can be incorrectly biased by expertise (e.g. geochemistry, geophysics), geographic location of focus, and the assumed conceptual model. The aim of this project is to develop a methodology for more objective geothermal exploration decision making at a given location, including go-no-go decision points to help developers and investors decide when to give up on a location. In this scope, two different approaches are investigated: 1) value of information analysis (VOIA) which is used for evaluating and quantifying the value of a data before they are purchased, and 2) enthalpy-based exploration targeting based on reservoir size, temperature gradient estimates, and internal rate of return (IRR). The first approach, VOIA, aims to identify the value of a particular data when making decisions with an uncertain outcome. This approach targets the pre-drilling phase of exploration. These estimated VOIs are highly affected by the size of the project and still have a high degree of subjectivity in assignment of probabilities. The second approach, exploration targeting, is focused on decision making during the drilling phase. It starts with a basic geothermal project definition that includes target and minimum required production capacity and initial budgeting for exploration phases. Then, it uses average temperature gradient, reservoir temperature estimates, and production capacity to define targets and go/no-go limits. The decision analysis in this approach is based on achieving a minimum IRR at each phase of the project. This second approach was determined to be less subjective, since it requires less subjectivity in the input values.

15 GEOTHERMAL ENERGY↗

Assessment of New Approaches in Geothermal Exploration Decision Making

Geothermal exploration projects have significant amount of risk associated with uncertainties encountered in the discovery of the geothermal resource. Understanding when and how to proceed in an exploration program, and when to walk away from a site, are two of the largest challenges for increased geothermal deployment. Current methodologies for exploration decision making is left to subjective by subjective expert opinion which can be incorrectly biased by expertise (e.g. geochemistry, geophysics), geographic location of focus, and the assumed conceptual model. The aim of this project is to develop a methodology for more objective geothermal exploration decision making at a given location, including go-no-go decision points to help developers and investors decide when to give up on a location. In this scope, two different approaches are investigated: 1) value of information analysis (VOIA) which is used for evaluating and quantifying the value of a data before they are purchased, and 2) enthalpy-based exploration targeting based on reservoir size, temperature gradient estimates, and internal rate of return (IRR). The first approach, VOIA, aims to identify the value of a particular data when making decisions with an uncertain outcome. This approach targets the pre-drilling phase of exploration. These estimated VOIs are highly affected by the size of the project and still have a high degree of subjectivity in assignment of probabilities. The second approach, exploration targeting, is focused on decision making during the drilling phase. It starts with a basic geothermal project definition that includes target and minimum required production capacity and initial budgeting for exploration phases. Then, it uses average temperature gradient, reservoir temperature estimates, and production capacity to define targets and go/no-go limits. The decision analysis in this approach is based on achieving a minimum IRR at each phase of the project. This second approach was determined to be less subjective, since it requires less subjectivity in the input values.

15 GEOTHERMAL ENERGY↗

Modeling electron temperature profiles in the pedestal with simple formulas for ETG transport

Abstract This paper reports on the refinement (building on (Hatch D.R. et al 2022 Phys. Plasmas 29 062501)) and application of simple formulas for electron heat transport from electron temperature gradient (ETG) driven turbulence in the pedestal. The formulas are improved by (1) improving the parameterization for certain key parameters and (2) carefully accounting for the impact of geometry and shaping in the underlying gyrokinetic simulation database. Comparisons with nonlinear gyrokinetic simulations of ETG transport in the MAST pedestal demonstrate the model’s applicability to spherical tokamaks in addition to standard aspect ratio tokamaks. We identify bounds for model applicability: the model is accurate in the steep gradient region, where the ETG turbulence is largely slab-like, but accuracy decreases as the temperature gradient becomes weaker in the pedestal top. We use the formula to model the electron temperature profile in the pedestal for four experimental scenarios while extensively varying input parameters to represent uncertainties. In all cases, the predicted electron temperature profile exhibits extreme sensitivity to separatrix temperature and density, which has implications for core-edge integration. The model reproduces the electron temperature profile for high η e = L n e / L T e scenarios but not for low η e scenarios in which microtearing modes (MTMs) have been identified. We develop a proof-of-concept model for MTM transport and explore the relative roles of ETG and MTM in setting the electron temperature profile.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Combined Structural Analysis of Core and Image Log of TGH 76-31 South East of Mt Baker, Washington State

Despite active volcanism, few geothermal energy resources have been developed in the Cascades Range. Temperature Gradient Hole 76-31 was drilled to ~440 m measured depth to probe for zones where fractures provide fluid conduits that transport deep volcanic heat to shallow depths that could support baseload, carbon neutral electrical generation. These zones were predicted by a Play Fairway assessment (PFA) of resource potential along a zone 11 km west-southwest of the summit of Mount Baker Volcano. Rock core, temperature logs, and an acoustic image log were obtained. By comparison to outcrops, the core has been initially interpreted as the Chilliwack group comprised of partially metamorphosed basaltic to andesitic volcanics. Core mapping reveals complex, steeply dipping networks of fractures and brecciation along slickensided strike slip faults; clay alteration is common in many of these structures. The majority of fractures are thoroughly healed by layers of chlorite and calcite; preservation of pyrite indicates anoxic conditions. The majority of fracture porosity resides in very dense fractures a few centimeters or less in length. The image log provides good insights into attitude of fractures that fully transect the core, but generally underestimates fracture density. The combination of complex, non-planar fracture zones containing many short fractures and healing promote misinterpretation of natural fracture attitude and density in the image log. The healing and anoxic minerals are consistent with the conductive temperature gradient measured in the well below a shallow isothermal zone, although, several fractures are open or only partially healed and resulted in fluid entries into the well. Here, the equilibrated measured temperature gradient of 64ºC/km and calculated heat flow of 145 mW/m2 is more than twice the regional average, indicating local influence of the Mt Baker magmatic system at the Little Park Creek TGH site.

Cascades↗

Gyrokinetic studies of core turbulence features in ASDEX Upgrade H-mode plasmas

Gyrokinetic validation studies are crucial for developing confidence in the model incorporated in numerical simulations and thus improving their predictive capabilities. As one step in this direction, we simulate an ASDEX Upgrade discharge with the GENE code, and analyze various fluctuating quantities and compare them to experimental measurements. The approach taken is the following. First, linear simulations are performed in order to determine the turbulence regime. Second, the heat fluxes in nonlinear simulations are matched to experimental fluxes by varying the logarithmic ion temperature gradient within the expected experimental error bars. Finally, the dependence of various quantities with respect to the ion temperature gradient is analyzed in detail. It is found that density and temperature fluctuations can vary significantly with small changes in this parameter, thus making comparisons with experiments very sensitive to uncertainties in the experimental profiles. However, cross-phases are more robust, indicating that they are better observables for comparisons between gyrokinetic simulations and experimental measurements.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Gyrokinetic GENE simulations of DIII-D near-edge L-mode plasmas

We present gyrokinetic simulations with the GENE code addressing the near-edge region of an L-mode plasma in the DIII-D tokamak. At radial position ρ = 0.80, simulations with the ion temperature gradient (ITG) increased by 40% above the nominal value give electron and ion heat fluxes that are in simultaneous agreement with the experiment. This gradient increase is consistent with the combined statistical and systematic uncertainty σ of the charge exchange recombination spectroscopy measurements at the 1.6σ level. Multiscale simulations are carried out with a realistic mass ratio and geometry for the first time in the near-edge. These multiscale simulations suggest that the highly unstable ion temperature gradient (ITG) modes of the flux-matched ion-scale simulations suppress electron-scale transport, such that ion-scale simulations are sufficient at this location. At radial position ρ = 0.90, nonlinear simulations show a hybrid state of ITG and trapped electron modes, which was not expected from linear simulations. The nonlinear simulations reproduce the total experimental heat flux with the inclusion of E × B shear effects and an increase in the electron temperature gradient by ∼23%. This gradient increase is compatible with the combined statistical and systematic uncertainty of the Thomson scattering data at the 1.3σ level. These results are consistent with previous findings that gyrokinetic simulations are able to reproduce the experimental heat fluxes by varying input parameters close to their experimental uncertainties, pushing the validation frontier closer to the edge region.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Thermal transpiration through single walled carbon nanotubes and graphene channels

Thermal transpiration through carbon nanotubes (CNTs) and graphene channels is studied using molecular dynamics (MD) simulations. The system consists of two reservoirs connected by a CNT. It is observed that a flow is developed inside the CNT from the low temperature reservoir to the high temperature reservoir when the two reservoirs are maintained at different temperatures. The influence of channel size and temperature gradient on the mean velocity is analysed by varying the CNT diameter and the temperature of one of the reservoirs. Larger flow rate is observed in the smaller diameter CNTs showing an increase in the mean velocity with increase in the temperature gradient. For the flow developed inside the CNTs, slip boundaries occur and the slip length is calculated using the velocity profile. We examine the effect of fluid-wall interaction strength (ε{sub fw}), diffusivity (D), and viscosity of the fluid (μ) on the temperature induced fluid transport through the CNTs. Similar investigations are also carried out by replacing the CNT with a graphene channel. Results show that the mean velocity of the fluid atoms in the graphene channel is lower than that through the CNTs. This can be attributed to the higher degree of confinement observed in the CNTs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Global gyrokinetic stability of collisionless microtearing modes in large aspect ratio tokamaks

Linear full radius gyrokinetic calculations show the existence of unstable microtearing modes (MTMs) in purely collisionless, high temperature, large aspect ratio tokamak plasmas. The present study takes into account fully gyrokinetic highly passing ions and electrons. The global 2-D structures of the collisionless mode with full radius coupling of the poloidal modes is obtained and compared with another electromagnetic mode, namely, the Alfvén Ion Temperature Gradient (AITG) mode (or Kinetic Ballooning Mode, KBM) for the same equilibrium profile. Several important characteristics of the modes are brought out and compared, such as a clear signature in the symmetry properties of the two modes, the plasma–β dependence, and radial and poloidal length scales of the electrostatic and magnetic vector potential fluctuations. Extensive parameter scans for this collisionless microtearing mode reveal the scaling of the growth rate with β and the electron temperature gradient η{sub e}. Scans at different β values show an inverse relationship between the η{sub e} threshold and β, leading to a stability diagram, and implying that the mode might exist at moderate to strong temperature gradients for finite β plasmas in large aspect ratio tokamaks. In contrast to small aspect ratio tokamaks where the trapped electron magnetic drift resonance is found to be important, in large aspect ratio tokamaks, a strong destabilization due to the magnetic drift resonance of passing electrons is observed and is identified as a possible collisionless drive mechanism for the collisionless MTM.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Generation and Life Cycle of Solar Spicules

The physical mechanism for the creation of solar spicules is proposed with three stages of their life cycle. It is assumed that at stage I the density hump is formed locally in the x-y plane in the lower chromosphere in the presence of temperature gradients of electrons and ions along the z-axis (the vertical direction). In this region, the density structure of quasi-neutral (n i ≃ n e = n) plasma after taking birth is accelerated in the vertical direction owing to the thermal force F th ∝ ∇n(x, y, t) × (∇T e + ∇T i ). The exact time-dependent analytical solution of two-fluid plasma equations is presented assuming that density is maximum at the center of the density structure and decays away from it gradually. The 2D density structure is created as a step function H(t) in time at the bottom of the chromosphere, and consequently, the vertical plasma velocity turns out to be the ramp function of time R(t) = tH(t), whereas the source term S(x, y, t) for the density follows the delta function δ(t) form. The upward acceleration a = a(x, y) $\hat{z}$ produced in this density structure is greater than the downward constant solar acceleration −g ⊙ in the chromosphere. In the transition region, the temperature gradients are steeper; therefore, the upward acceleration increases in magnitude g ⊙ ≪ a and the density hump spends less time there. This is stage II of its life cycle. In stage III, the density structure enters into the corona, where the gradients of temperatures vanish and the structure decelerates to zero velocity under the action of the solar gravitational force.

79 ASTRONOMY AND ASTROPHYSICS↗