SEARCH · Engineering Papers

Results for “phase kinetics”

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.

SourceResearch connectionFrom yearThrough year

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

At least 739 records · Page 41

All sources NASA NTRS DOE OSTI

NASA NTRS2021

Recent Advancements in Modeling and Simulation of Entry Systems at NASA

This paper describes recent development of modeling and simulation technologies for entry systems in support of NASA’s exploration missions. Mission-tailored research and development in modeling of entry systems occurs across the Agency (e.g., within the Orion and Mars 2020 Programs), however the aim of this paper is to discuss the broad, cross-mission research conducted by NASA’s Entry Systems Modeling (ESM) Project, which serves as the Agency’s only concerted effort toward advancing entry systems across a range of technical disciplines. Technology development in ESM is organized and prioritized from a system-level perspective, resulting in four broad technical areas of investment: (1) Predictive material modeling, (2) Shock layer kinetics and radiation, (3) Computational and experimental aerosciences, and (4) Guidance, navigation, and control. Investments in thermal protection material modeling are geared toward high-fidelity, predictive models capable of handling complex structures, with an eye toward optimizing design performance and quantifying thermal protection system reliability. New computational tools have been developed to characterize material properties and behavior at the microstructural level, and experimental techniques (molecular beam scattering, micro-computed tomography, among others) have been developed to measure material kinetics, morphology, and other parameters needed to inform and validate detailed simulations. Advancements have also been made in macrostructural simulation capability to enable 3-D system-scale calculations of material response with complex topological features, including differential recession of tile gaps. Research and development in the area of shock layer kinetics has focused on air and CO2-based atmospheres. Capacity and capability of the NASA Ames Electric Arc Shock Tube (EAST) have been expanded in recent years and analysis of resulting data has led to several improvements in kinetic models, while simultaneously reducing uncertainties associated with radiative heat transfer predictions. First-principles calculations of fundamental kinetic, thermodynamic, and transport data, along with state-specificmodels for non-equilibrium flow regimes, have also yielded new insights and have the potential to vastly improve model fidelity. Aerosciences is a very broad area of interest in entry systems, yet a number of important challenges are being addressed: Coupled fluid-structure simulations of parachute inflation and dynamics; Experimental and computational studies of vehicle dynamics; Multi-phase flow with dust particles to simulate entry environments at Mars during dust storms; Studies of roughness-induced heating augmentation relevant to tiled and woven thermal protection systems; and Advanced numerical methods to optimize computational analyses for desired accuracy versus cost. Guidance and control in the context of entry systems has focused on development of methods for multi-axis control (i.e. pitch and yaw, rather than bank angle alone) of spacecraft during entry and descent. With precision landing requirements driven by Mars human exploration goals, recent efforts have yielded 6-DOF models of multi-axis control with propulsive descent of both inflatable and rigid ellipsled-like architectures. Results for both configurations have demonstrated the ability to land within the 50-meter precision requirement demanded by Mars human exploration missions, while also reducing propellant requirements by enabling more efficient control through entry and descent. Ongoing research in GN&C is developing mechanical specifications for the systems and establishing engineering feasibility.

aerothermodynamics↗

NASA NTRS1976

The cause of the nova outburst

A large number of models are evolved for thermonuclear runaways in the hydrogen-rich envelopes of 1.00-solar-mass carbon-oxygen white dwarfs. Models characterized by enhanced CNO abundances satisfy the observations of the common nova outburst, ejecting from 10 to the 27th to 10 to the 29th power g at velocities of 200 to 2400 km/s and kinetic energies of 10 to the 44th to 10 to the 45th power erg. The theoretical light curves are similar to the observed light curves of common novae during the early stages of the outbursts. Explanations are given for the continuous ejection of mass which is observed for long times after the initial outbursts, for the relationship between maximum magnitude and the decline to minimum, and for the constant luminosity phase of the outburst and the oval shapes of the ejected nebulae. The analysis is extended to models with extreme enhancements of C-12 and to models which include infalling material in the evolution. The extreme C-12 studies result in outbursts which reach near-supernova proportions, while the accretion models result in light curves which resemble observed light curves quite closely. The accretion studies also demonstrate the need for enhanced abundances.

Starrfield, S.↗

NASA NTRS1992

Microwave Electrothermal Propulsion for Space

The microwave electrothermal thruster (MET) concept for medium or high-power spacecraft propulsion is described. The MET employs continuous wave microwave energy to create and maintain a plasma discharge in a flowing propellant gas. The discharge then acts to absorb the applied microwave energy and transform it into thermal and internal energy of the propellant. Expansion and expulsion of the hot propellant through a throat and nozzle finally converts the energy of the gas into thrust. The MET concept is electrodeless, synergistically combines high pressure and high power capability, provides external control over the energy-conversion discharge, and operates on hydrogen propellant. The potential performance of the MET on hydrogen propellant has been modeled with a two-dimensional kinetics computer code. The MET concept is particularly suitable for use with a magnetic nozzle. Apparatus is described for testing the resonant-cavity MET to power levels of 30 kW at 915 MHz on nitrogen, helium, and hydrogen. The low-ripple operation of the microwave generator has been verified, as has a procedure for starting the microwave discharge and raising the power applied to the cavity via a phase shifter-tuner.

Power, John L.↗

NASA NTRS2002

Tetragonal Lysozyme Nucleation and Crystal Growth: The Role of the Solution Phase

Lysozyme, and most particularly the tetragonal form of the protein, has become the default standard protein for use in macromolecule crystal nucleation and growth studies. There is a substantial body of experimental evidence, from this and other laboratories, that strongly suggests this proteins crystal nucleation and growth is by addition of associated species that are preformed by standard reversible concentration-driven self association processes in the bulk solution. The evidence includes high resolution AFM studies of the surface packing and of growth unit size at incorporation, fluorescence resonance energy transfer measurements of intermolecular distances in dilute solution, dialysis kinetics, and modeling of the growth rate data. We have developed a selfassociation model for the proteins crystal nucleation and growth. The model accounts for the obtained crystal symmetry, explains the observed surface structures, and shows the importance of the symmetry obtained by self-association in solution to the process as a whole. Further, it indicates that nucleation and crystal growth are not distinct mechanistically, but identical, with the primary difference being the probability that the particle will continue to grow or dissolve. This model also offers a possible mechanism for fluid flow effects on the growth process and how microgravity may affect it. While a single lysozyme molecule is relatively small (M.W. = 14,400), a structured octamer in the 4(sub 3) helix configuration (the proposed average sized growth unit) would have a M.W. = 115,000 and dimensions of 5.6 x 5.6 x 7.6 nm. Direct AFM measurements of growth unit incorporation indicate that units as wide as 11.2 nm and as long as 11.4 nm commonly attach to the crystal. These measurements were made at approximately saturation conditions, and they reflect the sizes of species that both added or desorbed from the crystal surface. The larger and less isotropic the associated species the more likely that it will be oriented to some degree in a flowing boundary layer, even at the low flow velocities measured about macromolecule crystals. Flow-driven effects resulting in misorientation upon addition to and incorporation into the crystal need only be a small fraction of a percentage to significantly affect the resulting crystal. One Earth, concentration gradient driven flow will maintain a high interfacial concentration, i.e., a high level (essentially that of the bulk solution) of solute association at the interface and higher growth rate. Higher growth rates mean an increased probability that misaligned growth units are trapped by subsequent growth layers before they can be desorbed and try again, or that the desorbing species will be smaller than the adsorbing species. In microgravity the extended diffusive boundary layer will lower the interfacial concentration. This results in a net dissociation of aggregated species that diffuse in from the bulk solution, i.e., smaller associated species, which are more likely able to make multiple attempts to correctly bind, yielding higher quality crystals.

Pusey, Marc L.↗

NASA NTRS2007

Global Simulation of Electromagnetic Ion Cyclotron Waves

It is well known that the effects of electromagnetic ion cyclotron (EMIC) waves on ring current (RC) ion and radiation belt (RB) electron dynamics strongly depend on such particle/wave characteristics as the phase-space distribution function, frequency, wave-normal angle, wave energy, and the form of wave spectral energy density. The consequence is that accurate modeling of EMIC waves and RC particles requires robust inclusion of the interdependent dynamics of wave growth/damping, wave propagation, and particles. Such a self-consistent model is being progressively developed by Khazanov et al. [2002 - 2007]. This model is based on a system of coupled kinetic equations for the RC and EMIC wave power spectral density along with the ray tracing equations. We will discuss the recent progress in understanding EMIC waves formation mechanisms in the inner magnetosphere. This problem remains unsettled in spite of many years of experimental and theoretical studies. Modern satellite observations by CRRES, Polar and Cluster still do not reveal the whole picture experimentally since they do not stay long enough in the generation region to give a full account of all the spatio-temporal structure of EMIC waves. The complete self-consistent theory taking into account all factors significant for EMIC waves generation remains to be developed. Several mechanisms are discussed with respect to formation of EMIC waves, among them are nonlinear modification of the ionospheric reflection by precipitating energetic protons, modulation of ion-cyclotron instability by long-period (Pc3/4) pulsations, reflection of waves from layers of heavy-ion gyroresonances, and nonlinearities of wave generation process. We show that each of these mechanisms have their attractive features and explains certain part experimental data but any of them, if taken alone, meets some difficulties when compared to observations. We conclude that development of a refined nonlinear theory and further correlated analysis of modern satellite and ground-based data is needed to solve this very intriguing problem.

Khazanov, G. V.↗

NASA NTRS2019

Recent Advancements in Modeling and Simulation of Entry Systems at NASA

This paper describes recent development of modeling and simulation technologies for entry systems in support of NASA's exploration missions. Mission-tailored research and development in modeling of entry systems occurs across the Agency (e.g., within the Orion and Mars 2020 Programs), however the aim of this paper is to discuss the broad, cross-mission research conducted by NASA's Entry Systems Modeling (ESM) Project, which serves as the Agency's only concerted effort toward advancing entry systems across a range of technical disciplines. Technology development in ESM is organized and prioritized from a system-level perspective, resulting in four broad technical areas of investment: (1) Predictive material modeling, (2) Shock layer kinetics and radiation, (3) Computational and experimental aerosciences, and (4) Guidance, navigation, and control. Investments in thermal protection material modeling are geared toward high-fidelity, predictive models capable of handling complex structures, with an eye toward optimizing design performance and quantifying thermal protection system reliability. New computational tools have been developed to characterize material properties and behavior at the microstructural level, and experimental techniques (molecular beam scattering, micro-computed tomography, among others) have been developed to measure material kinetics, morphology, and other parameters needed to inform and validate detailed simulations. Advancements have also been made in macrostructural simulation capability to enable 3-D system-scale calculations of material response with complex topological features, including differential recession of tile gaps. Research and development in the area of shock layer kinetics has focused on air and CO2-based atmospheres. Capacity and capability of the NASA Ames Electric Arc Shock Tube (EAST) have been expanded in recent years and analysis of resulting data has led to several improvements in kinetic models, while simultaneously reducing uncertainties associated with radiative heat transfer predictions. First-principles calculations of fundamental kinetic, thermodynamic, and transport data, along with state-specific models for non-equilibrium flow regimes, have also yielded new insights and have the potential to vastly improve model fidelity. Aerosciences is a very broad area of interest in entry systems, yet a number of important challenges are being addressed: Coupled fluid-structure simulations of parachute inflation and dynamics; Experimental and computational studies of vehicle dynamics; Multi-phase flow with dust particles to simulate entry environments at Mars during dust storms; Studies of roughness-induced heating augmentation relevant to tiled and woven thermal protection systems; and Advanced numerical methods to optimize computational analyses for desired accuracy versus cost. Guidance and control in the context of entry systems has focused on development of methods for multi-axis control (i.e. pitch and yaw, rather than bank angle alone) of spacecraft during entry and descent. With precision landing requirements driven by Mars human exploration goals, recent efforts have yielded 6-DOF models of multi-axis control with propulsive descent of both inflatable and rigid ellipsled-like architectures.

Barnhardt, Michael D.↗

NASA NTRS1985

Interdiffusional effects between tungsten fibers and an iron-nickel-base alloy

Tungsten fibers in the INCOLOY 903 alloy were annealed for over 100 hours at 1038 C and 1200 C. It was found that interdiffusion results in the formation of a reaction zone. SEM-EDS probe analysis showed that the chemistries across this zone were constant, suggesting the zone was a compound phase. The composition of the compound was estimated to be that of a mu-type phase. The local chemistry (in atomic percent) at the reaction zone/alloy matrix interface was found to be approximately 8 pct W, 1.2 pct Nb, 40 pct Fe, 14 pct Co, and 36 pct Ni. In addition, recrystallization was observed in both the remaining tungsten fiber and the nearby INCOLOY 903 matrix after annealing at 1200 C, but not at 1038 C. The results of this study suggest that reaction zone growth kinetics can be minimized by the reduction of Co and Fe and the increase of W in the matrix alloy.

Caulfield, T.↗

NASA NTRS1999

Buoyancy Driven Shear Flows of Bubble Suspensions

In this work the gas volume fraction and the root-mean-squared fluid velocity are measured in buoyancy driven shear flows of bubble suspensions in a tall, inclined, rectangular channel. The experiments are performed under conditions where We << 1a nd Re >> 1, for which comparisons are made with kinetic theory and numerical simulations. Here Re = gamma(a(exp 2)/nu is the Reynolds number and We = rho(gamma(exp 2))a(exp 3)/sigma is the Weber number; gamma is the shear rate, a is the bubble radius, nu is the kinematic viscosity of the liquid, rho is the density of the liquid, and sigma is the surface tension of the gas/liquid interface. Kang et al. calculated the bubble phase pressure and velocity variance of sheared bubble suspensions under conditions where the bubbles are spherical and the liquid phase velocity field can be approximated using potential flow theory, i.e. We= 0 and Re >> 1. Such conditions can be achieved in an experiment using gas bubbles, with a radius of O(0.5mm), in water. The theory requires that there be no average relative motion of the gas and liquid phases, hence the motivation for an experimental program in microgravity. The necessity of performing preliminary, Earth based experiments, however, requires performing experiments where the gas phase rises in the liquid, which significantly complicates the comparison of experiments with theory. Rather than comparing experimental results with theory for a uniform, homogeneous shear flow, experiments can be compared directly with solutions of the averaged equations of motion for bubble suspensions. This requires accounting for the significant lift force acting on the gas phase when the bubbles rise parallel to the average velocity of the sheared suspension. Shear flows can be produced in which the bubble phase pressure gradient, arising from shear induced collisions amongst the bubbles, balances a body force (centrifugal or gravitational) on the gas phase. A steady, non-uniform gas volume fraction can be measured, from which the bubble phase pressure gradient can be obtained and compared to theory and numerical simulations. The presence of bounding walls further complicates the experiments, since the detailed interactions of the bubbles with bounding walls is not well understood, especially in the presence of gravity, where the momentum and energy exchange depends on the inclination of the wall.

Koch, D. L.↗

NASA NTRS2014

Mass Dependency of Isotope Fractionation of Gases Under Thermal Gradient and Its Possible Implications for Planetary Atmosphere Escaping Process

Physical processes that unmix elements/isotopes of gas molecules involve phase changes, diffusion (chemical or thermal), effusion and gravitational settling. Some of those play significant roles for the evolution of chemical and isotopic compositions of gases in planetary bodies which lead to better understanding of surface paleoclimatic conditions, e.g. gas bubbles in Antarctic ice, and planetary evolution, e.g. the solar-wind erosion induced gas escaping from exosphere on terrestrial planets.. A mass dependent relationship is always expected for the kinetic isotope fractionations during these simple physical processes, according to the kinetic theory of gases by Chapman, Enskog and others [3-5]. For O-bearing (O16, -O17, -O18) molecules the alpha O-17/ alpha O-18 is expected at 0.5 to 0.515, and for S-bearing (S32,-S33. -S34, -S36) molecules, the alpha S-33/ αlpha S-34 is expected at 0.5 to 0.508, where alpha is the isotope fractionation factor associated with unmixing processes. Thus, one isotope pair is generally proxied to yield all the information for the physical history of the gases. However, we recently] reported the violation of mass law for isotope fractionation among isotope pairs of multiple isotope system during gas diffusion or convection under thermal gradient (Thermal Gradient Induced Non-Mass Dependent effect, TGI-NMD). The mechanism(s) that is responsible to such striking observation remains unanswered. In our past studies, we investigated polyatomic molecules, O2 and SF6, and we suggested that nuclear spin effect could be responsible to the observed NMD effect in a way of changing diffusion coefficients of certain molecules, owing to the fact of negligible delta S-36 anomaly for SF6.. On the other hand, our results also showed that for both diffusion and convection under thermal gradient, this NMD effect is increased by lower gas pressure, bigger temperature gradient and lower average temperature, which indicate that the nuclear spin effect may not be the significant contributor as the energies involved in the hyperfine effect are much smaller than those with molecular collisions, especially under convective conditions.

Sun, Tao↗

NASA NTRS2016

Preferential Heating of Oxygen 5+ Ions by Finite-Amplitude Oblique Alfven Waves

Minor ions in the fast solar wind are known to have higher temperatures and to flow faster than protons in the interplanetary space. In this study we combine previous research on parametric instability theory and 2.5D hybrid simulations to study the onset of preferential heating of Oxygen 5+ ions by large-scale finite-amplitude Alfven waves in the collisionless fast solar wind. We consider initially non-drifting isotropic multi-species plasma, consisting of isothermal massless fluid electrons, kinetic protons and kinetic Oxygen 5+ ions. The external energy source for the plasma heating and energization are oblique monochromatic Alfven-cyclotron waves. The waves have been created by rotating the direction of initial parallel pump, which is a solution of the multi-fluid plasma dispersion relation. We consider propagation angles theta less than or equal to 30 deg. The obliquely propagating Alfven pump waves lead to strong diffusion in the ion phase space, resulting in highly anisotropic heavy ion velocity distribution functions and proton beams. We discuss the application of the model to the problems of preferential heating of minor ions in the solar corona and the fast solar wind.

Maneva, Yana G.↗

NASA NTRS1983

Kinetics of copper ion absorption by cross-linked calcium polyacrylate membranes

The absorption of copper ions from aqueous copper acetate solutions by cross-linked calcium acrylate membranes was found to obey parabolic kinetics similar to that found for oxidation of metals that form protective oxide layers. For pure calcium polyacrylate membranes the rate constant was essentially independent of copper acetate concentration and film thickness. For a cross-linked copolymer film of polyvinyl alcohol and calcium polyacrylate, the rate constant was much greater and dependent on the concentration of copper acetate. The proposed mechanism in each case involves the formation of a copper polyacrylate phase on the surface of the membrane. The diffusion of the copper ion through this phase appears to be the rate controlling step for the copolymer film. The diffusion of the calcium ion is apparently the rate controlling step for the calcium polyacrylate. At low pH, the copper polyacrylate phase consists of the normal copper salt; at higher pH, the phase appears to be the basic copper salt.

Philipp, W. H.↗

NASA NTRS1992

A semikinetic model for early stage plasmasphere refilling. I - Effects of Coulomb collisions

A collisionless, time-dependent, kinetic plasma model is applied to the problem of baseline plasmasphere refilling of an initially depleted flux tube, without regard for the effects of wave-particle interactions. Refilling calculations for various flux tubes and for different ionospheric plasma fluxes and temperatures are performed. In each case considered, the same set of events occurs. Initially, two polar wind outflows develop from each hemisphere and set up counterstreaming beams. With time the vacant phase space region between these beams fills, primarily because of collision-induced particle diffusion but also because of lowering ambipolar potential drops from the increasing density in the plasmasphere. In contrast to all previous hydrodynamic approaches, no formation of shocks was found. The plasma first evolves an isotropic, nearly Maxwellian velocity distribution in a region that starts near the ionosphere and moves outward toward the equator. For reasonable topside ionospheric temperatures and fluxes, the thermal plasma all along an L shell is found to become nearly isotropic in 6 to 30 hr, consistent with the observations of Horwitz et al. (1984).

Wilson, G. R.↗

NASA NTRS2001

A Self-Consistent Model of the Interacting Ring Current Ions and Electromagnetic ICWs. Initial Results: Waves and Precipitation Fluxes

Initial results from the new developed model of the interacting ring current ions and ion cyclotron waves are presented. The model described by the system of two bound kinetic equations: one equation describes the ring current ion dynamics, and another one gives wave evolution. Such system gives a self-consistent description of the ring current ions and ion cyclotron waves in a quasilinear approach. Calculating ion-wave relationships, on a global scale under non steady-state conditions during May 2-5, 1998 storm, we presented the data at three time cuts around initial, main, and late recovery phases of May 4, 1998 storm phase. The structure and dynamics of the ring current proton precipitating flux regions and the wave active ones are discussed in detail.

Khazanov, G. V.↗

NASA NTRS1976

A kinetic study of the interaction between atomic oxygen and aerosols

This study was concerned with the effects of NH4Cl and (NH4)2SO4 aerosols on the kinetics of disappearance of atomic oxygen. Atomic oxygen was generated by a 2.45-GHz microwave discharge and the kinetics of disappearance measured in a fast flow system using NO2 titration. Values of the recombination coefficient for heterogeneous wall recombination were determined for clean, H2SO4-coated, and (NH4)2SO4-coated Pyrex to be 0.000050, 0.000020, and 0.000019, respectively. A rapid exothermic chemical reaction was found to occur between atomic oxygen and an NH4Cl wall coating; the products were NH3, NO, H2O, and HCl. The NH4Cl aerosol was generated by gas phase reaction of NH3 with HCl. The aerosol particles were approximately spherical and nearly monodisperse with a mean diameter of 1.6 plus or minus 0.2 micron. The rate constant for the disappearance of atomic oxygen in the presence of NH4Cl aerosol was measured. No significant decrease was observed in the rate of disappearance of atomic oxygen in the presence of an (NH4)2SO4 aerosol at a concentration of 285 mg per cu m.

Akers, F. I.↗

NASA NTRS1988

Crystallization kinetics of BaO-Al2O3-SiO2 glasses

Barium aluminosilicate glasses are being investigated as matrix materials in high-temperature ceramic composites for structural applications. Kinetics of crystallization of two refractory glass compositions in the barium aluminosilicate system were studied by differential thermal analysis (DTA), X-ray diffraction (XRD), and scanning electron microscopy (SEM). From variable heating rate DTA, the crystallization activation energies for glass compositions (wt percent) 10BaO-38Al2O3-51SiO2-1MoO3 (glass A) and 39BaO-25Al2O3-35SiO2-1MoO3 (glass B) were determined to be 553 and 558 kJ/mol, respectively. On thermal treatment, the crystalline phases in glasses A and B were identified as mullite (3Al2O3-2SiO2) and hexacelsian (BaO-Al2O3-2SiO2), respectively. Hexacelsian is a high-temperature polymorph which is metastable below 1590 C. It undergoes structural transformation into the orthorhombic form at approximately 300 C accompanied by a large volume change which is undesirable for structural applications. A process needs to be developed where stable monoclinic celsian, rather than hexacelsian, precipitates out as the crystal phase in glass B.

Bansal, Narottam P.↗

NASA NTRS1989

Crystallization kinetics of BaO-Al2O3-SiO2 glasses

Bansal, Narottam P.↗

NASA NTRS1989

Production of oxygen from lunar ilmenite

The overall objective of this project was to develop a novel carbothermal reduction process for production of oxygen from lunar ilmenite. The specific objective was to use a reaction sequence in which a wide variety of carbonaceous compounds (including carbonaceous wastes) can be used as reducing agents. During the first phase, two reactor systems were designed, constructed, and operated to study the reaction fundamental important in this process. One system is a small fluidized bed, and the other is a thermo-gravimetric reactor system. Preliminary experiments on synthetic ilmenite are conducted to study the effect of carbon type, carbon loading, temperature, and gas flow rate. Results indicate that a reaction path based on carbon gasification can be used to promote the overall kinetics. A unique temperature and concentration-programmed reaction procedure was being developed for rapid parametric study of the process.

Shadman, F.↗

NASA NTRS1992

Inertial mode oscillations of Jupiter

The properties of the inertial modes of Jupiter are investigated using several different models for that planet. The inertial modes are rotationally induced oscillation modes for which the kinetic energy generally dominates the potential energy of oscillation. The frequency spectrum of the inertial modes mainly depends on the density stratification of Jupiter and sensitively reflects the existence or nonexistence of density discontinuities in the interior. A particularly interesting consequence of the calculations is that observations of the inertial oscillations of Jupiter may enable us to determine whether or not the dense hydrogen in the envelope of this planet undergoes the plasma phase transition (PPT). This may provide an astrophysical test of current theories of the thermodynamic properties of dense hydrogen. It is also found that the discontinuity modes associated with the PPT have observable amplitdues at the surface. These modes may provide an independent test of the interior structure of Jupiter.

Lee, Umin↗