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All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Epitaxial solar cells fabrication

Silicon epitaxy has been studied for the fabrication of solar cell structures, with the intent of optimizing efficiency while maintaining suitability for space applications. SiH2CL2 yielded good quality layers and junctions with reproducible impurity profiles. Diode characteristics and lifetimes in the epitaxial layers were investigated as a function of epitaxial growth conditions and doping profile, as was the effect of substrates and epitaxial post-gettering on lifetime. The pyrolytic decomposition of SiH4 was also used in the epitaxial formation of highly doped junction layers on bulk Si wafers. The effects of junction layer thickness and bulk background doping level on cell performance, in particular, open-circuit voltage, were investigated. The most successful solar cells were fabricated with SiH2 CL2 to grow p/n layers on n(+) substrates. The best performance was obtained from a p(+)/p/n/n(+) structure grown with an exponential grade in the n-base layer.

Daiello, R. V.↗
NASA NTRS1988

Instability and sound emission from a flow over a curved surface

The growth and decay of a wavepacket convecting in a boundary layer over a concave-convex surface is studied numerically using direct computations of the Navier-Stokes equations. The resulting sound radiation is computed using the linearized Euler equations with the pressure from the Navier-Stokes solution as a time-dependent boundary condition. It is shown that on the concave portion the amplitude of the wavepacket increases and its bandwidth broadens while on the convex portion some of the components in the packet are stabilized. The pressure field decays exponentially away from the surface and then algebraically exhibits a decay characteristic of acoustic waves in two dimensions. The far-field acoustic pressure exhibits a peak at a frequency corresponding to the inflow instability frequency.

Maestrello, L.↗
NASA NTRS2007

A Start Toward Micronucleus-Based Decompression Models; Altitude Decompression

Do gaseous micronuclei trigger the formation of bubbles in decompression sickness (DCS)? Most previous instructions for DCS prevention have been oriented toward supersaturated gas in tissue. We are developing a mathematical model that is oriented toward the expected behavior of micronuclei. The issue is simplified in altitude decompressions because the aviator or astronaut is exposed only to decompression, whereas in diving there is a compression before the decompression. The model deals with four variables: duration of breathing of 100% oxygen before going to altitude (O2 prebreathing), altitude of the exposure, exposure duration, and rate of ascent. Assumptions: a) there is a population of micronuclei of various sizes having a range of characteristics, b) micronuclei are stable until they grow to a certain critical nucleation radius, c) it takes time for gas to diffuse in or out of micronuclei, and d) all other variables being equal, growth of micronuclei upon decompression is more rapid at high altitude because of the rarified gas in the micronuclei. To estimate parameters, we use a dataset of 4,756 men in altitude chambers exposed to various combinations of the model s variables. The model predicts occurrence of DCS symptoms quite well. It is notable that both the altitude chamber data and the model show little effect of O2 prebreathing until it lasts more than 60 minutes; this is in contrast to a conventional idea that the benefit of prebreathing is directly due to exponential washout of tissue nitrogen. The delay in response to O2 prebreathing can be interpreted as time required for outward diffusion of nitrogen; when the micronuclei become small enough, they are disabled, either by crushing or because they cannot expand to a critical nucleation size when the subject ascends to altitude.

Van Liew, H. D.↗
NASA NTRS2003

Common Ion Effects In Zeoponic Substrates: Dissolution And Cation Exchange Variations Due to Additions of Calcite, Dolomite and Wollastonite

c1inoptilolite-rich tuff-hydroxyapatite mixture (zeoponic substrate) has the potential to serve as a synthetic soil-additive for plant growth. Essential plant macro-nutrients such as calcium, phosphorous, magnesium, ammonium and potassium are released into solution via dissolution of the hydroxyapatite and cation exchange on zeolite charged sites. Plant growth experiments resulting in low yield for wheat have been attributed to a Ca deficiency caused by a high degree of cation exchange by the zeolite. Batch-equilibration experiments were performed in order to determine if the Ca deficiency can be remedied by the addition of a second Ca-bearing, soluble, mineral such as calcite, dolomite or wollastonite. Variations in the amount of calcite, dolomite or wollastonite resulted in systematic changes in the concentrations of Ca and P. The addition of calcite, dolomite or wollastonite to the zeoponic substrate resulted in an exponential decrease in the phosphorous concentration in solution. The exponential rate of decay was greatest for calcite (5.60 wt. % -I), intermediate for wollastonite (2.85 wt.% -I) and least for dolomite (1.58 wt.% -I). Additions of the three minerals resulted in linear increases in the calcium concentration in solution. The rate of increase was greatest for calcite (3.64), intermediate for wollastonite (2.41) and least for dolomite (0.61). The observed changes in P and Ca concentration are consistent with the solubilities of calcite, dolomite and wollastonite and with changes expected from a common ion effect with Ca. Keywords: zeolite, zeoponics, common-ion effect, clinoptilolite, hydroxyapatite

Beiersdorfer, R. E.↗
NASA NTRS2020

Plant responses to rising vapor pressure deficit

Recent decades have been characterized by increasing temperatures worldwide, resulting in an exponential climb in vapor pressure deficit (VPD). VPD has been identified as an increasingly important driver of plant functioning in terrestrial biomes and has been established as a major contributor in recent drought‐induced plant mortality independent of other drivers associated with climate change. Despite this, few studies have isolated the physiological response of plant functioning to high VPD, thus limiting our understanding and ability to predict future impacts on terrestrial ecosystems. An abundance of evidence suggests that stomatal conductance declines under high VPD and transpiration increases in most species up until a given VPD threshold, leading to a cascade of subsequent impacts including reduced photosynthesis and growth, and higher risks of carbon starvation and hydraulic failure. Incorporation of photosynthetic and hydraulic traits in ‘next‐generation’ land‐surface models has the greatest potential for improved prediction of VPD responses at the plant‐ and global‐scale, and will yield more mechanistic simulations of plant responses to a changing climate. By providing a fully integrated framework and evaluation of the impacts of high VPD on plant function, improvements in forecasting and long‐term projections of climate impacts can be made.

mortality↗
NASA NTRS1995

Effects of alpha-particles on survival and chromosomal aberrations in human mammary epithelial cells

We have studied the radiation responses of a human mammary epithelial cell line, H184B5 F5-1 M/10. This cell line was derived from primary mammary cells after treatment with chemicals and heavy ions. The F5-1 M/10 cells are immortal, density-inhibited in growth, and non-tumorigenic in athymic nude mice and represent an in vitro model of the human epithelium for radiation studies. Because epithelial cells are the target of alpha-particles emitted from radon daughters, we concentrated our studies on the efficiency of alpha-particles. Confluent cultures of M/10 cells were exposed to accelerated alpha-particles [beam energy incident at the cell monolayer = 3.85 MeV, incident linear energy transfer (LET) in cell = 109 keV/microns] and, for comparison, to 80 kVp x-rays. The following endpoints were studied: (1) survival, (2) chromosome aberrations at the first postirradiation mitosis, and (3) chromosome alterations at later passages following irradiation. The survival curve was exponential for alpha-particles (D0 = 0.73 +/- 0.04 Gy), while a shoulder was observed for x-rays (alpha/beta = 2.9 Gy; D0 = 2.5 Gy, extrapolation number 1.6). The relative biological effectiveness (RBE) of high-LET alpha-particles for human epithelial cell killing was 3.3 at 37% survival. Dose-response curves for the induction of chromosome aberrations were linear for alpha-particles and linearquadratic for x-rays. The RBE for the induction of chromosome aberrations varied with the type of aberration scored and was high (about 5) for chromosome breaks and low (about 2) for chromosome exchanges.(ABSTRACT TRUNCATED AT 250 WORDS).

NASA Center JSC↗
NASA NTRS2013

Rain Characteristics and Large-Scale Environments of Precipitation Objects with Extreme Rain Volumes from TRMM Observations

This study adopts a "precipitation object" approach by using 14 years of Tropical Rainfall Measuring Mission (TRMM) Precipitation Feature (PF) and National Centers for Environmental Prediction (NCEP) reanalysis data to study rainfall structure and environmental factors associated with extreme heavy rain events. Characteristics of instantaneous extreme volumetric PFs are examined and compared to those of intermediate and small systems. It is found that instantaneous PFs exhibit a much wider scale range compared to the daily gridded precipitation accumulation range. The top 1% of the rainiest PFs contribute over 55% of total rainfall and have 2 orders of rain volume magnitude greater than those of the median PFs. We find a threshold near the top 10% beyond which the PFs grow exponentially into larger, deeper, and colder rain systems. NCEP reanalyses show that midlevel relative humidity and total precipitable water increase steadily with increasingly larger PFs, along with a rapid increase of 500 hPa upward vertical velocity beyond the top 10%. This provides the necessary moisture convergence to amplify and sustain the extreme events. The rapid increase in vertical motion is associated with the release of convective available potential energy (CAPE) in mature systems, as is evident in the increase in CAPE of PFs up to 10% and the subsequent dropoff. The study illustrates distinct stages in the development of an extreme rainfall event including: (1) a systematic buildup in large-scale temperature and moisture, (2) a rapid change in rain structure, (3) explosive growth of the PF size, and (4) a release of CAPE before the demise of the event.

TRMM↗
NASA NTRS2025

Time-Dependent Satellite Explosion Probabilities for Long-Term Orbital Debris Environment Modeling

On-orbit accidental explosions are a significant contributor to the growth of the orbital debris population. Certain types of satellites have been seen to exhibit different behaviors and timelines of explosions. Recent assessments of on-orbit explosions for three categories of satellites – Russian Sistema Obespecheniya Zapuska (SOZ, Proton 4th stage attitude and ullage motors) units, spacecraft, and rocket bodies – suggest that on-orbit explosions can be modeled using a continuous, time-dependent probability of explosion. This paper discusses the methodology for developing a time-dependent probability of explosion as a function of the satellite’s orbital lifetime based on historical explosions. The SOZ units are found to be best modeled by a modified Gaussian probability distribution, with the peak probability of explosion occurring around 10.4 years on-orbit. Spacecraft and rocket bodies both exhibit exponentially decaying explosion probabilities, with rocket bodies showing fast-, medium-, and slow-time modes of decay. Total cumulative probabilities of explosion are approximately 57% for SOZ units, 4% for spacecraft, and 2% for rocket bodies. Examples of implementation in a simulation of the orbital debris environment using NASA's long-term evolutionary model are given, showing the overall explosion behavior over two centuries is significantly different from that using a previously implemented constant-probability type-dependent explosion rate model and provides a better representation of the historical explosion record.

Alyssa P Manis↗
NASA NTRS2002

Observations and Parameterizations of Particle Size Distributions in Deep Tropical Cirrus and Stratiform Precipitation Clouds: Results from In-Situ Observations in TRMM Field Campaigns

In this study, we report on the evolution of particle size distributions (PSDs) and habits as measured during slow, Lagrangian-type spiral descents through deep subtropical and tropical cloud layers in Florida, Brazil, and Kwajalein, Marshall Islands, most of which were precipitating. The objective of the flight patterns was to learn more about how the PSDs evolved in the vertical and to obtain information of the vertical structure of microphysical properties. New instrumentation yielding better information on the concentrations of particles in the size (D) range between 0.2 and 2 cm, as well as improved particle imagery, produced more comprehensive observations for tropical stratiform precipitation regions and anvils than have been available previously. Collocated radar observations provided additional information on the vertical structure of the cloud layers sampled. Most of the spirals began at cloud top, with temperatures (T) as low as -50 C, and ended at cloud base or below the melting layer (ML). The PSDs broadened from cloud top towards cloud base, with the largest particles increasing in size from several millimeters at cloud top to one centimeter or larger towards cloud base. Some continued growth was noted in the upper part of the ML. Concentrations of particles less than 1 mm in size decreased with decreasing height. The result was a consistent change in the PSDs in the vertical. Similarly, systematic changes in the size dependence of the particle cross-sectional area was noted with decreasing height. Aggregation-as ascertained from both the changes in the PSDs and evolution of particle habits as observed in high detail with the cloud particle imager (CPI) probe-was responsible for these trends. The PSDs were generally well-represented by gamma distributions of the form N = N0 gamma D microns e- lambda gamma D that were fitted to the PSDs over 1-km horizontal intervals throughout the spirals. The intercept (N0 gamma), slope (lambda gamma), and dispersion (microns) values were derived for each PSD. Exponential curves (N = N0e- lambdaD; micron = 0) were also fitted to the distributions. The lambda gamma values for given spirals varied systematically with temperature as did the values of lambda (exponential), and the data generally conformed to values found in previous studies involving exponential fits to size distributions in mid-latitude frontal and cirrus layers. Considerable variability often noted in the PSD properties during the loops of individual spirals was manifested primarily in large changes in N0 gamma and N0, but micron, lambda gamma and lambda remained fairly stable. Temperature is not found to be the sole factor controlling lambda gamma or lambda but is a primary one. Direct relationships were found between lambda gamma and N0 gamma or lambda gamma and micron for the gamma distributions and lambda and N0 for the exponential. The latter relationship was not found as distinctly in earlier studies; observed PSDs in this study had better fidelity with less scatter. The micron values changed monotonically with T over the range of temperatures and were directly related to N0 gamma or lambda gamma, thereby reducing the number of variables in the PSD functional equation to two. In the upper part of the ML, N0 and lambda continued to decrease, and in the lower part these values began to increase as the largest particles melted. We developed general expressions relating various bulk microphysical, radar, and radiative transfer-related variables to N0 gamma and lambda gamma, useful for both tropical and mid-latitude clouds. These relationships facilitate the specification of a number of bulk properties in cloud and climate models. The results presented in this paper apply best to temperatures between 0 and -40 C, for which the measured radar reflectivities fall in the range of 0 to 25 dBZe.

Heymsfield, Andrew J.↗
NASA NTRS1999

Elevation Change of the Southern Greenland Ice Sheet from Satellite Radar Altimeter Data

Long-term changes in the thickness of the polar ice sheets are important indicators of climate change. Understanding the contributions to the global water mass balance from the accumulation or ablation of grounded ice in Greenland and Antarctica is considered crucial for determining the source of the about 2 mm/yr sea-level rise in the last century. Though the Antarctic ice sheet is much larger than its northern counterpart, the Greenland ice sheet is more likely to undergo dramatic changes in response to a warming trend. This can be attributed to the warmer Greenland climate, as well as a potential for amplification of a global warming trend in the polar regions of the Northern Hemisphere. In collaboration with Drs. Curt Davis and Craig Kluever of the University of Missouri, we are using data from satellite radar altimeters to measure changes in the elevation of the Southern Greenland ice sheet from 1978 to the present. Difficulties with systematic altimeter measurement errors, particularly in intersatellite comparisons, beset earlier studies of the Greenland ice sheet thickness. We use altimeter data collected contemporaneously over the global ocean to establish a reference for correcting ice-sheet data. In addition, the waveform data from the ice-sheet radar returns are reprocessed to better determine the range from the satellite to the ice surface. At JPL, we are focusing our efforts principally on the reduction of orbit errors and range biases in the measurement systems on the various altimeter missions. Our approach emphasizes global characterization and reduction of the long-period orbit errors and range biases using altimeter data from NASA's Ocean Pathfinder program. Along-track sea-height residuals are sequentially filtered and backwards smoothed, and the radial orbit errors are modeled as sinusoids with a wavelength equal to one revolution of the satellite. The amplitudes of the sinusoids are treated as exponentially-correlated noise processes with a time-constant of six days. Measurement errors (e.g., altimeter range bias) are simultaneously recovered as constant parameters. The corrections derived from the global ocean analysis are then applied over the Greenland ice sheet. The orbit error and measurement bias corrections for different missions are developed in a single framework to enable robust linkage of ice-sheet measurements from 1978 to the present. In 1998, we completed our re-evaluation of the 1978 Seasat and 1985-1989 Geosat Exact Repeat Mission data. The estimates of ice thickness over Southern Greenland (south of 72N and above 2000 m) from 1978 to 1988 show large regional variations (+/-18 cm/yr), but yield an overall rate of +1.5 +/- 0.5 cm/yr (one standard error). Accounting for systematic errors, the estimate may not be significantly different from the null growth rate. The average elevation change from 1978 to 1988 is too small to assess whether the Greenland ice sheet is undergoing a long-term change.

Haines, Bruce J.↗
NASA NTRS2000

The Use of Ferrofluids to Model Materials Processing (MSFC Center Director's Discretionary Fund)

Many crystals grown in space have structural flaws believed to result from convective motions during the growth phase. The character of these instabilities is not well understood but is associated with thermal and solutal density variations near the solidification interface in the presence of residual gravity and g-jitter. To study these instabilities in a separate, controlled space experiment, a concentration gradient would first have to be artificially established in a timely manner as an initial condition. This is generally difficult to accomplish in a microgravity environment because the momentum of the fluid injected into a test cell tends to swirl around and mix in the absence of a restoring force. The use of magnetic fields to control the motion and position of liquids has received recent, growing interest. The possibility of using the force exerted by a non-uniform magnetic field on a ferrofluid to not only achieve fluid manipulation but also to actively control fluid motion makes it an attractive candidate for space applications. This paper describes a technique for quickly establishing a linear or exponential fluid concentration gradient using a magnetic field in place of gravity to stabilize the deployment. Also discussed is a photometric technique for measuring the concentration profile using light attenuation. Although any range of concentrations can be realized, photometric constraints impose some limitations on measurements. Results of the ground-based experiments indicate that the species distribution is within 3 percent of the predicted value.

Leslie, F.↗
NASA NTRS2000

A Technique for Rapidly Deploying a Concentration Gradient with Applications to Microgravity

The latter half of the last century has seen rapid advancements in semiconductor crystal growth powered by the demand for high performance electronics in myriad applications. The reduced gravity environment of space has also been used for crystal growth tests, especially in instances where terrestrial growth has largely been unsuccessful. While reduced gravity crystal growth affords some control of the gravity parameter, many crystals grown in space, to date, have structural flaws believed to result from convective motions during the growth phase. The character of these instabilities is not well understood but is associated with thermal and solutal density variations near the solidification interface in the presence of residual gravity and g-jitter. In order to study these instabilities in a separate, controlled space experiment, a concentration gradient would first have to be artificially established in a timely manner as an initial condition. This is generally difficult to accomplish in a microgravity environment because the momentum of the fluid injected into a test cell tends to swirl around and mix in the absence of a restoring force. The use of magnetic fields to control the motion and position of liquids has received growing interest in recent times. The possibility of using the force exerted by a non-uniform magnetic field on a ferrofluid to not only achieve fluid manipulation but also to actively control fluid motion makes it an attractive candidate for space applications. This paper describes a technique for quickly establishing a linear or exponential fluid concentration gradient using a magnetic field in place of gravity to stabilize the deployment. Also discussed is a photometric technique for measuring the concentration profile using light attenuation. Results of the ground-based experiments indicate that the concentration distribution is within 3% of the predicted value. Although any range of concentations can be realized, photometric constraints are discussed which impose some limitations on measurements.

Leslie, Fred↗
NASA NTRS2016

Application of X-Ray Pulsar Navigation: A Characterization of the Earth Orbit Trade Space

The potential for pulsars as a navigation source has been studied since their discovery in 1967. X-ray pulsar navigation (XNAV) is a celestial navigation system that uses the consistent timing nature of x-ray photons from milli-second pulsars (MSP) to perform space navigation. By comparing the detected arrival of x-ray photons to a reference database of expected pulsar lightcurve timing models, one can infer a range and range rate measurement based on light time delay. Much of the challenge of XNAV comes from the faint signal, availability, and distant nature of pulsars. This is a study of potential pulsar XNAV measurements to measure extended Kalman filter (EKF) tracking performance with a wide trade space of bounded Earth orbits, using a simulation of existing x-ray detector space hardware. An example of an x-ray detector for XNAV is the NASA Station Explorer for X-ray Timing and Navigation (SEXTANT) mission, a technology demonstration of XNAV set to perform on the International Space Station (ISS) in late 2016early 2017. XNAV hardware implementation is driven by trajectory and environmental influences which add noise to the x-ray pulse signal. In a closed Earth orbit, the radiation environment can exponentially increase the signal noise from x-ray pulsar sources, decreasing the quality and frequency of measurements. The SEXTANT mission in particular improves on the signal to noise ratio by focusing an array of 56 x-ray silicon drift detectors at one pulsar target at a time. This reduces timing glitches and other timing noise contributions from ambient x-ray sources to within a 100 nanosecond resolution. This study also considers the SEXTANT scheduling challenges inherent in a single target observation. Finally, as the navigation sources are now relatively inertial targets, XNAV measurements are also subject to periods of occultation from various celestial bodies. This study focuses on the characterization of these drivers in closed Earth orbits and is not a tuning analysis of the EKF. The study shows that the closed Earth orbit for XNAV performance is reliant on the orbit semi-major axis and eccentricity as well as orbit inclination. These parameters are the primary drivers of pulsar measurement availability and significantly influence the natural spacecraft orbit dynamics. Sensitivity to initial orbit determination error growth due to the scarcity of XNAV measurements within an orbital period require appropriate timing of initial XNAV measurements. The orbit angles of argument of perigee and right ascension of the ascending node, alongside the other orbit parameters, complete the initial cadence of XNAV measurements. The performance of initial XNAV measurements then propagates throughout the experimental period. The study provides a basis to missions who wish to consider XNAV as a potential navigation source in a closed Earth orbit design. It provides a family of orbit trajectories as well as other modeling considerations needed to effectively evaluate if XNAV is an effective navigation source for a potential mission. As an EKF is sensitive to a linearized estimated state, this study has a direct benefit of providing effective XNAV measurements to maintain spacecraft tracking, independent of other navigation sources. In the particular use case of the SEXTANT mission, it also provides a novel scheduling algorithm which addresses the need to prioritize and manage pulsar observations for effective navigation.

PULSAR↗
NASA NTRS2016

Application of X-Ray Pulsar Navigation: A Characterization of the Earth Orbit Trade Space

The potential for pulsars as a navigation source has been studied since their discovery in 1967. X-ray pulsar navigation (XNAV) is a celestial navigation system that uses the consistent timing nature of x-ray photons from millisecond pulsars (MSP) to perform space navigation. By comparing the detected arrival of x-ray photons to a reference database of expected pulsar light-curve timing models, one can infer a range and range rate measurement based on light time delay. Much of the challenge of XNAV comes from the faint signal, availability, and distant nature of pulsars. This is a study of potential pulsar XNAV measurements to measure extended Kalman filter (EKF) tracking performance with a wide trade space of bounded Earth orbits, using a simulation of existing x-ray detector space hardware. An example of an x-ray detector for XNAV is the NASA Station Explorer for X-ray Timing and Navigation (SEXTANT) mission, a technology demonstration of XNAV set to perform on the International Space Station (ISS) in late 2016early 2017. XNAV hardware implementation is driven by trajectory and environmental influences which add noise to the x-ray pulse signal. In a closed Earth orbit, the radiation environment can exponentially increase the signal noise from x-ray pulsar sources, decreasing the quality and frequency of measurements. The SEXTANT mission in particular improves on the signal to noise ratio by focusing an array of 56 x-ray silicon drift detectors at one pulsar target at a time. This reduces timing glitches and other timing noise contributions from ambient x-ray sources to within a 100 nanosecond resolution. This study also considers the SEXTANT scheduling challenges inherent in a single target observation. Finally, as the navigation sources are now relatively inertial targets, XNAV measurements are also subject to periods of occultation from various celestial bodies. This study focuses on the characterization of these drivers in closed Earth orbits and is not a tuning analysis of the EKF. The study shows that the closed Earth orbit for XNAV performance is reliant on the orbit semi-major axis and eccentricity as well as orbit inclination. These parameters are the primary drivers of pulsar measurement availability and significantly influence the natural spacecraft orbit dynamics. Sensitivity to initial orbit determination error growth due to the scarcity of XNAV measurements within an orbital period require appropriate timing of initial XNAV measurements. The orbit angles of argument of perigee and right ascension of the ascending node, alongside the other orbit parameters, complete the initial cadence of XNAV measurements. The performance of initial XNAV measurements then propagates throughout the experimental period. The study provides a basis to missions who wish to consider XNAV as a potential navigation source in a closed Earth orbit design. It provides a family of orbit trajectories as well as other modeling considerations needed to effectively evaluate if XNAV is an effective navigation source for a potential mission. As an EKF is sensitive to a linearized estimated state, this study has a direct benefit of providing effective XNAV measurements to maintain spacecraft tracking, independent of other navigation sources. In the particular use case of the SEXTANT mission, it also provides a novel scheduling algorithm which addresses the need to prioritize and manage pulsar observations for effective navigation.

x-ray↗
NASA NTRS1994

Nonlinear instability of accelerating shock waves with application to supernovae

We consider the stability of a planar accelerating shock front in an exponential atmosphere, a situation that can be described by a self-similar solution. A previous linear instability analysis showed that there are three regimes, depending on the wavelength of the perturbation along the direction of the shock front: at long wavelengths the shock is unstable, at intermediate wavelengths it is overstable, and at short wavelenghts it is stable, where the characteristic length is set by the initial density scale height. We have carried out numerical simulations of such an accelerating shock front and have confirmed the results of the semianalytic linear analysis in the linear regime. In the nonlinear regime, the evolution again depends on the three wavelength domains. At long wavelengths, the instability continuously grows but the flow remains smooth, and at short wavelengths, the flow is stable. The intermediate wavelength, overstable regime shows more complex evolution. The growing linear oscillations saturate soon after entering the nonlinear regime and the oscillations continue with the same approximate period. The shock front develops moving points of intersection, which generate weak shock fronts and density and pressure structure in the immediate postshock flow. The density fluctuations, with a contrast of a factor of 2-3, become frozen into the downstream flow. The growth of the instability is slow, so substantial initial perturbations are needed; thesemay be present in Type II supernovae with red supergiant progenitor stars which have outer convective regions. The clumping in the outer supernova atmosphere may affect spectral line formation and may play a role in the formation of fast knots.

Luo, Ding↗