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NASA NTRS2022

Simulated Lunar Surface Hydration Measurements using Multispectral Lidar at 3 µm

Accurately measuring the variability of spectroscopic signatures of hydration (H2O + OH) on the illuminated lunar surface at 3 µm as a function of latitude, lunar time of day, and composition is crucial to determining the generation and destruction mechanisms of OH species and understanding the global water cycle. A prime complication in analysis of the spectroscopic feature is the accurate removal of thermal emission, which can modify or even eliminate the hydration feature depending on the data processing methods used and assumptions made. An orbital multispectral lidar, with laser illumination at key diagnostic wavelengths, would provide uniform, zero-phase geometry, complete latitude and time of day coverage from a circular polar orbit, and is agnostic to the thermal state of the surface. We have performed measurement simulations of a four-wavelength multispectral lidar using spectral mixtures of hydrated mid-ocean ridge basalt (MORB) glasses and lunar regolith endmembers to assess the lidar performance in measuring hydration signatures on the lunar surface. Our results show a feasible system with wavelengths at 1.5 µm, 2.65 µm, 2.8 µm, and 3.1 µm can measure lunar hydration with a precision of 52 ppm (1σ) or better. These results, combined with the uniform measurement capabilities of multispectral lidar make it a valuable spectroscopic technique for elucidating mechanisms of OH/H2O generation, migration, and destruction.

D. R. Cremons↗

NASA NTRS1975

Modal equations for cellular convection

We expand the fluctuating flow variables of Boussinesq convection in the planform functions of linear theory. Our proposal is to consider a drastic truncation of this expansion as a possible useful approximation scheme for studying cellular convection. With just one term included, we obtain a fairly simple set of equations which reproduces some of the qualitative properties of cellular convection and whose steady-state form has already been derived by Roberts (1966). This set of 'modal equations' is analyzed at slightly supercritical and at very high Rayleigh numbers. In the latter regime the Nusselt number varies with Rayleigh number just as in the mean-field approximation with one horizontal scale when the boundaries are rigid. However, the Nusselt number now depends also on the Prandtl number in a way that seems compatible with experiment. The chief difficulty with the approach is the absence of a deductive scheme for deciding which planforms should be retained in the truncated expansion.

Gough, D. O.↗

NASA NTRS1993

The asymmetric wind of R127

We present optical, linear polarimetry in broad-band UBVRI filters plus narrow-band filters centered on the emission lines of H-alpha and the red forbidden N II and spectropolarimetry in the wavelength range from 4120 A to 6770 A of the luminous blue variable R127 in the LMC. Both observations display a decrease of the percentage polarization across the H-alpha emission line with respect to the continuum. We assume that H-alpha is recombination-line dominated and thus intrinsically unpolarized, and we use the continuum subtracted line polarization to estimate the interstellar foreground polarization. The resulting amount of intrinsic continuum polarization of R127 is very large, of order 1-1.5 percent, implying both the presence of copious free electrons and a considerable asphericity in their distribution. The two data sets, taken two months apart, display significant variations in the continuum polarization, which confirms that the stellar-wind properties of R127 are time-dependent in the maximum state. We discuss several possible wind geometries and present arguments favoring a clumpy, axisymmetric outflow.

Schulte-Ladbeck, R. E.↗

NASA NTRS2013

Photosynthesis-dependent Isoprene Emission from Leaf to Planet in a Global Carbon-chemistry-climate Model

We describe the implementation of a biochemical model of isoprene emission that depends on the electron requirement for isoprene synthesis into the FarquharBallBerry leaf model of photosynthesis and stomatal conductance that is embedded within a global chemistry-climate simulation framework. The isoprene production is calculated as a function of electron transport-limited photosynthesis, intercellular and atmospheric carbon dioxide concentration, and canopy temperature. The vegetation biophysics module computes the photosynthetic uptake of carbon dioxide coupled with the transpiration of water vapor and the isoprene emission rate at the 30 min physical integration time step of the global chemistry-climate model. In the model, the rate of carbon assimilation provides the dominant control on isoprene emission variability over canopy temperature. A control simulation representative of the present-day climatic state that uses 8 plant functional types (PFTs), prescribed phenology and generic PFT-specific isoprene emission potentials (fraction of electrons available for isoprene synthesis) reproduces 50 of the variability across different ecosystems and seasons in a global database of 28 measured campaign-average fluxes. Compared to time-varying isoprene flux measurements at 9 select sites, the model authentically captures the observed variability in the 30 min average diurnal cycle (R2 6496) and simulates the flux magnitude to within a factor of 2. The control run yields a global isoprene source strength of 451 TgC yr1 that increases by 30 in the artificial absence of plant water stress and by 55 for potential natural vegetation.

photosynthesis↗

NASA NTRS2020

“It’s Raining Bits”: Patterns in Directional Precipitation Persistence Across the United States

The spatial and temporal ordering of precipitation occurrence impacts ecosystems, streamflow, and water availability. For example, both large-scale climate patterns and local landscapes drive weather events, and the typical speeds and directions of these events moving across a basin dictate the timing of flows at its outlet. We address the predictability of precipitation occurrence at a given location, based on the knowledge of past precipitation at surrounding locations. We identify ‘‘dominant directions of precipitation influence’’ across the continental United States based on a gridded daily dataset. Specifically, we apply information theory–based measures that characterize dominant directions and strengths of spatial and temporal precipitation dependencies. On a national average, this dominant direction agrees with the prevalent direction of weather movement from west to east across the country, but regional differences reflect topographic divides, precipitation gradients, and different climatic drivers of precipitation. Trends in these information relationships and their correlations with climate indices over the past 70 years also show seasonal and spatial divides. This study expands upon a framework of information-based predictability to answer questions about spatial connectivity in addition to temporal persistence. The methods presented here are generally useful to understand many aspects of weather and climate variability.

North America↗

NASA NTRS1999

Satellite Data Assimilation

Satellite altimetry provides the only routine observation of a dynamic variable of the global ocean. For instance, measurements from the TOPEX/POSEIDON altimeter have provided dramatic basin-wide images of the space-time evolution of sea level associated with the 1997-98 El Nino event. The nature of large-scale ocean circulation is being studied that underlies such sea level changes measured by satellite altimetry. To first approximation, properties of large-scale (order 1000 km and larger) sea level variability is latitudinally dependent. An analysis using a general circulation model shows that sea level changes are largely due to wind-driven baroclinic (depth dependent) circulation in the tropics (within 20 degrees of the equator), but are primarily due to the expansion and contraction of near surface water in temperate latitudes (between 20 deg. and 40 deg.) forced by seasonal heating and cooling. In contrast, wind-driven barotropic (depth independent) circulation dominates sea level variability in high latitudes (40 deg. and higher) characterized by periods that are as short as a few days. The presence of such inhomogeneity and the significance of high-frequency, large-scale sea level changes had not been fully recognized prior to this study, and are summarized in Fukumori et al. Numerical models provide theoretical relationships among properties that can be inverted using observations so as to estimate the entire state of the ocean, including properties that are otherwise difficult to measure remotely. The process is data assimilation. An approximate Kalman filter and smoother have been devised to assimilate three years of TOPEX/POSEIDON sea level data into a global ocean general circulation model. The figure below demonstrates the skill of the assimilation, and shows the altimeter assimilated estimate being in closer agreement than the simulation is with independent in situ measurements of subsur ace temperature and velocity, consistent with formal uncertainty estimates. Results from this study have been summarized and submitted for publication. The study demonstrates the feasibility of global ocean data assimilation and illustrates applications in monitoring and understanding of processes controlling the evolution of the ocean. Additional information is contained in the original.

Fukumori, Ichiro↗

NASA NTRS1999

Improving Reanalyses Using TRMM and SSM/I-Derived Precipitation and Total Precipitable Water Observations

Global reanalyses currently contain significant errors in the primary fields of the hydrological cycle such as precipitation, evaporation, moisture, and the related cloud fields, especially in the tropics. The Data Assimilation Office (DAO) at the NASA Goddard Space Flight Center has been exploring the use of rainfall and total precipitable water (TPW) observations from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) and the Special Sensor Microwave/ Imager (SSM/I) instruments to improve these fields in reanalyses. The DAO has developed a "1+1"D procedure to assimilate 6-hr averaged rainfall and TPW into the Goddard Earth Observing System (GEOS) Data Assimilation System (DAS). The algorithm is based on a 6-hr time integration of a column version of the GEOS DAS. The "1+1" designation refers to one spatial dimension plus one temporal dimension. The scheme minimizes the least-square differences between the satellite-retrieved rain rates and those produced by the column model over the 6-hr analysis window. The control variables are analysis increments of moisture within the Incremental Analysis Update (IAU) framework of the GEOS DAS. This 1+1D scheme, in its generalization to four dimensions, is related to the standard 4D variational assimilation but differs in its choice of the control variable. Instead of estimating the initial condition at the beginning of the assimilation cycle, it estimates the constant IAU forcing applied over a 6-hr assimilation cycle. In doing so, it imposes the forecast model as a weak constraint in a manner similar to the variational continuous assimilation techniques. We present results from an experiment in which the observed rain rate and TPW are assumed to be "perfect". They show that assimilating the TMI and SSM/I-derived surface precipitation and TPW observations improves not only the precipitation and moisture fields but also key climate parameters directly linked to convective activities such as clouds, the outgoing longwave radiation, and the large-scale circulation in the tropics. In particular, assimilating these data types reduce the state-dependent systematic errors in the assimilated products. The improved analysis also leads to a better short-range forecast, but the impact is modest compared with improvements in the time-averaged fields. These results suggest that, in the presence of biases and other errors of the forecast model, it is possible to improve the time-averaged "climate content" in the assimilated data without comparable improvements in the short-range forecast skill. Results of this experiment provide a useful benchmark for evaluating error covariance models for optimal use of these data types.

Hou, Arthur Y.↗

NASA NTRS2015

Prediction of Tensile Strength of Friction Stir Weld Joints with Adaptive Neuro-Fuzzy Inference System (ANFIS) and Neural Network

Friction-stir-welding (FSW) is a solid-state joining process where joint properties are dependent on welding process parameters. In the current study three critical process parameters including spindle speed (𝑁), plunge force (𝐹𝑧), and welding speed (𝑉) are considered key factors in the determination of ultimate tensile strength (UTS) of welded aluminum alloy joints. A total of 73 weld schedules were welded and tensile properties were subsequently obtained experimentally. It is observed that all three process parameters have direct influence on UTS of the welded joints. Utilizing experimental data, an optimized adaptive neuro-fuzzy inference system (ANFIS) model has been developed to predict UTS of FSW joints. A total of 1200 models were developed by varying the number of membership functions (MFs), type of MFs, and combination of four input variables (𝑁,𝑉,𝐹𝑧,𝐸𝐹𝐼) utilizing a MATLAB platform. Note EFI denotes an empirical force index derived from the three process parameters. For comparison, optimized artificial neural network (ANN) models were also developed to predict UTS from FSW process parameters. By comparing ANFIS and ANN predicted results, it was found that optimized ANFIS models provide better results than ANN. This newly developed best ANFIS model could be utilized for prediction of UTS of FSW joints.

Mohammad W Dewan↗

NASA NTRS1983

Experimental philosophy leading to a small scale digital data base of the conterminous United States for designing experiments with remotely sensed data

Research using satellite remotely sensed data, even within any single scientific discipline, often lacked a unifying principle or strategy with which to plan or integrate studies conducted over an area so large that exhaustive examination is infeasible, e.g., the U.S.A. However, such a series of studies would seem to be at the heart of what makes satellite remote sensing unique, that is the ability to select for study from among remotely sensed data sets distributed widely over the U.S., over time, where the resources do not exist to examine all of them. Using this philosophical underpinning and the concept of a unifying principle, an operational procedure for developing a sampling strategy and formal testable hypotheses was constructed. The procedure is applicable across disciplines, when the investigator restates the research question in symbolic form, i.e., quantifies it. The procedure is set within the statistical framework of general linear models. The dependent variable is any arbitrary function of remotely sensed data and the independent variables are values or levels of factors which represent regional climatic conditions and/or properties of the Earth's surface. These factors are operationally defined as maps from the U.S. National Atlas (U.S.G.S., 1970). Eighty-five maps from the National Atlas, representing climatic and surface attributes, were automated by point counting at an effective resolution of one observation every 17.6 km (11 miles) yielding 22,505 observations per map. The maps were registered to one another in a two step procedure producing a coarse, then fine scale registration. After registration, the maps were iteratively checked for errors using manual and automated procedures. The error free maps were annotated with identification and legend information and then stored as card images, one map to a file. A sampling design will be accomplished through a regionalization analysis of the National Atlas data base (presently being conducted). From this analysis a map of homogeneous regions of the U.S.A. will be created and samples (LANDSAT scenes) assigned by region.

Labovitz, M. L.↗

NASA NTRS1998

Shuttle Mission STS-50: Orbital Processing of High-Quality CdTe Compound Semiconductors Experiment: Final Flight Sample Characterization Report

The Orbital Processing of High-Quality Doped and Alloyed CdTe Compound Semiconductors program was initiated to investigate, quantitatively, the influences of gravitationally dependent phenomena on the growth and quality of bulk compound semiconductors. The objective was to improve crystal quality (both structural and compositional) and to better understand and control the variables within the crystal growth production process. The empirical effort entailed the development of a terrestrial (one-g) experiment baseline for quantitative comparison with microgravity (mu-g) results. This effort was supported by the development of high-fidelity process models of heat transfer, fluid flow and solute redistribution, and thermo-mechanical stress occurring in the furnace, safety cartridge, ampoule, and crystal throughout the melting, seeding, crystal growth, and post-solidification processing. In addition, the sensitivity of the orbital experiments was analyzed with respect to the residual microgravity (mu-g) environment, both steady state and g-jitter. CdZnTe crystals were grown in one-g and in mu-g. Crystals processed terrestrially were grown at the NASA Ground Control Experiments Laboratory (GCEL) and at Grumman Aerospace Corporation (now Northrop Grumman Corporation). Two mu-g crystals were grown in the Crystal Growth Furnace (CGF) during the First United States Microgravity Laboratory Mission (USML-1), STS-50, June 24 - July 9, 1992.

Larson, David J.↗

NASA NTRS2002

Comparison of Two Methods for Estimating the Sampling-Related Uncertainty of Satellite Rainfall Averages Based on a Large Radar Data Set

The uncertainty of rainfall estimated from averages of discrete samples collected by a satellite is assessed using a multi-year radar data set covering a large portion of the United States. The sampling-related uncertainty of rainfall estimates is evaluated for all combinations of 100 km, 200 km, and 500 km space domains, 1 day, 5 day, and 30 day rainfall accumulations, and regular sampling time intervals of 1 h, 3 h, 6 h, 8 h, and 12 h. These extensive analyses are combined to characterize the sampling uncertainty as a function of space and time domain, sampling frequency, and rainfall characteristics by means of a simple scaling law. Moreover, it is shown that both parametric and non-parametric statistical techniques of estimating the sampling uncertainty produce comparable results. Sampling uncertainty estimates, however, do depend on the choice of technique for obtaining them. They can also vary considerably from case to case, reflecting the great variability of natural rainfall, and should therefore be expressed in probabilistic terms. Rainfall calibration errors are shown to affect comparison of results obtained by studies based on data from different climate regions and/or observation platforms.

Lau, William K. M.↗

NASA NTRS2016

Space Weathering of Olivine: Samples, Experiments and Modeling

Olivine is a major constituent of chondritic bodies and its response to space weathering processes likely dominates the optical properties of asteroid regoliths (e.g. S- and many C-type asteroids). Analyses of olivine in returned samples and laboratory experiments provide details and insights regarding the mechanisms and rates of space weathering. Analyses of olivine grains from lunar soils and asteroid Itokawa reveal that they display solar wind damaged rims that are typically not amorphized despite long surface exposure ages, which are inferred from solar flare track densities (up to 10 (sup 7 y)). The olivine damaged rim width rapidly approaches approximately 120 nm in approximately 10 (sup 6 y) and then reaches steady-state with longer exposure times. The damaged rims are nanocrystalline with high dislocation densities, but crystalline order exists up to the outermost exposed surface. Sparse nanophase Fe metal inclusions occur in the damaged rims and are believed to be produced during irradiation through preferential sputtering of oxygen from the rims. The observed space weathering effects in lunar and Itokawa olivine grains are difficult to reconcile with laboratory irradiation studies and our numerical models that indicate that olivine surfaces should readily blister and amorphize on relatively short time scales (less than 10 (sup 3 y)). These results suggest that it is not just the ion fluence alone, but other variable, the ion flux that controls the type and extent of irradiation damage that develops in olivine. This flux dependence argues for caution in extrapolating between high flux laboratory experiments and the natural case. Additional measurements, experiments, and modeling are required to resolve the discrepancies among the observations and calculations involving solar wind processing of olivine.

Keller, L. P.↗

NASA NTRSDate not supplied

Early Information Parameter-Set Analysis for Satellite Close Approaches using Machine Learning

Understanding orbital mechanics is essential in space flight and navigation applications, and leveraging modern force models for flight path projection remains an important aspect in space mission design and operation. However, force models do not capture all the dynamics or perturbations in the space environment and thus are subject to errors in predicting the state vectors. The further out the predicted miss distance between spacecraft is from the time of closest approach (TCA), the larger the propagated errors in the predicted miss distance at TCA is. The dependency on these force models for spacecraft flight state prediction calls for a more reliable method that can quantify, or even reduce, these propagated errors. With recent advances in the field artificial intelligence, specifically in machine and deep learning algorithms, a model that implements these approaches can improve on the modern force model approach. The goal for this work is to provide an early-information decision-making threshold, in order to prioritize risk assessment implementation, given the ongoing increase of space objects. In analyzing the relationship of several parameters from conjunction data messages(CDMs) and solar information, early information becomes viable in miss distance prediction with unsupervised learning techniques, which learn the parameters that are linked together with miss distance and probability of collision (Pc) variables. Another approach implemented for identifying relationships within CDMs is supervised learning, in which a shallow neural network binary classifier learns to distinguish events with Pc values¡108. These parameters detected in the unsupervised process are then applied to a regression neural network, which predicts the miss distance at TCA for a specific event within a given uncertainty bound. For the regression neural network, a Long Short Term Memory (LSTM) neural network is implemented, which yields memory about each time step in an event. Using an LSTM network, the model learns to predict miss distance within 0.2km of the value measured at TCA. Although there is a limited amount of "close miss" data to train a network, the network learns to associate parameters, like large energy dissipation rates with the secondary object, with an elevated Pc

Brianna I. Robertson↗

NASA NTRS2015

Stability of ENSO and Its Tropical Pacific Teleconnections over the Last Millennium

Determining past changes in the amplitude, frequency and teleconnections of the El Nio Southern Oscillation (ENSO) is important for understanding its potential sensitivity to future anthropogenic climate change. Palaeo-reconstructions from proxy records provide long-term information of ENSO interactions with the background climatic state through time. However, it remains unclear how ENSO characteristics have changed through time, and precisely which signals proxies record. Proxy interpretations are underpinned by the assumption of stationarity in relationships between local and remote climates, and often utilise archives from single locations located in the Pacific Ocean to reconstruct ENSO histories. Here, we investigate the stationarity of ENSO teleconnections using the Last Millennium experiment of CMIP5 (Coupled Model Intercomparison Project phase 5) (Taylor et al., 2012). We show that modelled ENSO characteristics vary on decadal- to centennial-scales, resulting from internal variability and external forcings, such as tropical volcanic eruptions. Furthermore, the relationship between ENSO conditions and local climates across the Pacific basin varies throughout the Last Millennium. Results show the stability of teleconnections is regionally dependent and proxies may reveal complex changes in teleconnected patterns, rather than large-scale changes in base ENSO characteristics. As such, proxy insights into ENSO likely require evidence to be synthesised over large spatial areas in order to deconvolve changes occurring in the NINO3.4 region from those pertaining to proxy-relevant local climatic variables. To obtain robust histories of the ENSO and its remote impacts, we recommend interpretations of proxy records should be considered in conjunction with palaeo-reconstructions from within the Central Pacific

teleconnections↗

NASA NTRS2015

Global Ocean Evaporation: How Well Can We Estimate Interannual to Decadal Variability?

Evaporation from the world's oceans constitutes the largest component of the global water balance. It is important not only as the ultimate source of moisture that is tied to the radiative processes determining Earth's energy balance but also to freshwater availability over land, governing habitability of the planet. Here we focus on variability of ocean evaporation on scales from interannual to decadal by appealing to three sources of data: the new MERRA-2 (Modern-Era Retrospective analysis for Research and Applications -2); climate models run with historical sea-surface temperatures, ice and atmospheric constituents (so-called AMIP experiments); and state-of-the-art satellite retrievals from the Seaflux and HOAPS (Hamburg Ocean-Atmosphere Parameters and Fluxes from Satellite) projects. Each of these sources has distinct advantages as well as drawbacks. MERRA-2, like other reanalyses, synthesizes evaporation estimates consistent with observationally constrained physical and dynamical models-but data stream discontinuities are a major problem for interpreting multi-decadal records. The climate models used in data assimilation can also be run with lesser constraints such as with SSTs and sea-ice (i.e. AMIPs) or with additional, minimal observations of surface pressure and marine observations that have longer and less fragmentary observational records. We use the new ERA-20C reanalysis produced by ECMWF embodying the latter methodology. Still, the model physics biases in climate models and the lack of a predicted surface energy balance are of concern. Satellite retrievals and comparisons to ship-based measurements offer the most observationally-based estimates, but sensor inter-calibration, algorithm retrieval assumptions, and short records are dominant issues. Our strategy depends on maximizing the advantages of these combined records. The primary diagnostic tool used here is an analysis of bulk aerodynamic computations produced by these sources and uses a first-order Taylor series analysis of wind speed, SST, near-surface stability and relative humidity variations around climatology to gauge the importance of these components. We find that the MERRA-2 evaporation record is strongly influenced by the availability of wind speed and humidity from passive microwave imagers beginning in the late 1980s as well as by the SST record. The trend over the period 1980 to present is nearly 10%. AMIP or the ERA-20C trends are much smaller. We find that ENSO-related signals involving both wind speed and thermodynamic variability remain the primary signal in the latter and are confirmed by satellite retrievals. We present uncertainty estimates based on the various data sources and discuss the implications for GEWEX water and energy budget science challenges.

Robertson, Franklin R.↗

NASA NTRS2019

Soil Moisture Data Assimilation

Accurate knowledge of soil moisture at the continental scale is important for improving predictions of weather, agricultural productivity and natural hazards, but observations of soil moisture at such scales are limited to indirect measurements, either obtained through satellite remote sensing or from meteorological networks. Land surface models simulate soil moisture processes, using observation-based meteorological forcing data, and auxiliary information about soil, terrain and vegetation characteristics. Enhanced estimates of soil moisture and other land surface variables, along with their uncertainty, can be obtained by assimilating observations of soil moisture into land surface models. These assimilation results are of direct relevance for the initialization of hydro-meteorological ensemble forecasting systems. The success of the assimilation depends on the choice of the assimilation technique, the nature of the model and the assimilated observations, and, most importantly, the characterization of model and observation error. Systematic differences between satellite-based microwave observations or satellite-retrieved soil moisture and their simulated counterparts require special attention. Other challenges include inferring root-zone soil moisture information from observations that pertain to a shallow surface soil layer, propagating information to unobserved areas and downscaling of coarse information to finer-scale soil moisture estimates. This chapter summarizes state-of-the-art solutions to these issues with conceptual data assimilation examples, using techniques ranging from simplified optimal interpolation to spatial ensemble Kalman filtering. In addition, operational soil moisture assimilation systems are discussed that support numerical weather prediction at ECMWF and provide value-added soil moisture products for the NASA Soil Moisture Active Passive mission.

radar backscatter↗

NASA NTRS1980

Overview of Boeing supersonic transport efforts, 1971 - 1979

Following cancellation of the United States Supersonic Transport program, the status of the technology was assessed carefully and emphasis was put on finding solutions for what were considered the major technical difficulties. In particular, work on the breakthroughs needed to advance the technology was emphasized. Currently, solutions to all major technical problems are identified. Depending on the subject, either the problem is no longer a concern or the steps needed to bring about a solution are mapped out clearly. Throughout the NASA SCR program, important strides were made in the identification of design advances which would greatly improve supersonic airplane fuel efficiency, noise, and other performance and cost affecting parameters. Furthermore, these efforts created an atmosphere in which it was possible for new ideas to flourish and positive inventions to take place such as the variable cycle engine and the blended fuselage. These technical gains show that, given availability of such technology, advanced supersonic transports could be developed that would be economically successful and environmentally acceptable.

Sigalla, A.↗

NASA NTRS1997

Numerical Modeling of Tidal Effects in Polytropic Accretion Disks

A two-dimensional time-dependent hybrid Fourier-Chebyshev method of collocation is developed and used for the study of tidal effects in accretion disks, under the assumptions of a polytropic equation of state and a standard alpha viscosity prescription. Under the influence of the m = 1 azimuthal component of the tidal potential, viscous oscillations in the outer disk excite an m = 1 eccentric instability in the disk. While the m = 2 azimuthal component of the tidal potential excites a Papaloizou-Pringle instability in the inner disk (a saturated m = 2 azimuthal mode), with an elliptic pattern rotating at about a fraction (approx. = 1/3) of the local Keplerian velocity in the inner disk. The period of the elliptic mode corresponds well to the periods of the short-period oscillations observed in cataclysmic variables. In cold disks (r(Omega)/c(sub s) = M approx. = 40) we also find a critical value of the viscosity parameter (alpha approx. = 0.01), below which shock dissipation dominates and is balanced by the wave amplification due to the wave action conservation. In this case the double spiral shock propagates all the way to the inner boundary with a Mach number M(sub s) approx. = 1.3.

Godon, Patrick↗