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94 records · Page 6

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NASA NTRS1994

Advanced data assimilation in strongly nonlinear dynamical systems

Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.

Miller, Robert N.↗

NASA NTRS1995

Turbulence in the solar wind: Kinetic effects

Although a casual look at the fluctuating magnetic and velocity fields in the solar wind may be reminiscent of a chaotic and disordered flow, there is, nonetheless. considerable organization and structure in the temporal and spatial evolution of those fluctuations. Much of that evolution is controlled by processes operating on rather large scales for example, in the inner heliosphere, the fluctuations in magnetic and velocity are highly correlated in the sense of outward propagating Alfven waves. This correlation can be destroyed both in time and distance by the velocity gradients present between fast and slow streams and by other nonlinear processes which stir the medium, producing a turbulent cascade of energy from large to small scales. Many aspects of this turbulent evolution can be described using fluid models; however, at some scale the fluid approximation breaks down and a more detailed paradigm is necessary. The breakdown is evident in the power spectrum of magnetic fluctuations at scales approaching the wavelength of ion cyclotron waves. At those scales, as evident in Mariner 10 and other magnetometer data, the spectrum bends over and the fluctuations damp, possibly heating the ambient plasma. Some evidence for heating of the solar wind is present in the Voyager data. Fluid models can be modified to some extent to incorporate aspects of a kinetic treatment. This is done by modifying the dissipation terms in the fluid equations and by including extra terms, such as the Hall term. As the scale lengths of phenomena shrink further and approach the spatial and temporal scales characteristic of electron phenomena, the fluid description must be abandoned altogether and a fully kinetic treatment is required. One example is the generation of Langmuir solitons produced by the electron beams that generate type 3 solar radio bursts.

Goldstein, M. L.↗

NASA NTRS1995

Investigation of computational and spectral analysis methods for aeroacoustic wave propagation

Most computational fluid dynamics (CFD) schemes are not adequately accurate for solving aeroacoustics problems, which have wave amplitudes several orders of magnitude smaller yet with frequencies larger than the flow field variations generating the sound. Hence, a computational aeroacoustics (CAA) algorithm should have minimal dispersion and dissipation features. A dispersion relation preserving (DRP) scheme is, therefore, applied to solve the linearized Euler equations in order to simulate the propagation of three types of waves, namely: acoustic, vorticity, and entropy waves. The scheme is derived using an optimization procedure to ensure that the numerical derivatives preserve the wave number and angular frequency of the partial differential equations being discretized. Consequently, simulated waves propagate with the correct wave speeds and exhibit their appropriate properties. A set of radiation and outflow boundary conditions, compatible with the DRP scheme and derived from the asymptotic solutions of the governing equations, are also implemented. Numerical simulations are performed to test the effectiveness of the DRP scheme and its boundary conditions. The computed solutions are shown to agree favorably with the exact solutions. The major restriction appears to be that the dispersion relations can be preserved only for waves with wave lengths longer than four or five spacings. The boundary conditions are found to be transparent to the outgoing disturbances. However, when the disturbance source is placed closer to a boundary, small acoustic reflections start appearing. CAA generates enormous amounts of temporal data which needs to be reduced to understand the physical problem being simulated. Spectral analysis is one approach that helps us in extracting information which often can not be easily interpreted in the time domain. Thus, three different methods for the spectral analysis of numerically generated aeroacoustic data are studied. First, the capabilities of two traditional methods for spectral analysis, namely, the Blackman-Tukey method and periodogram method, are compared in estimating the spectra of a simple-periodic process. The periodogram is then applied to analyze transitory-deterministic processes. Finally, these two methods are compared with a more recent method, referred as the Weighted-Overlapped-Segment-Averaging (WOSA) method, in estimating the spectra of a chaotic (random-like) process. From the demonstrative case for the spectral analyses of data generated by simple-periodic process, the periodogram method is found to give a better estimate of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window is found to perform better with the periodogram method than with the Blackman-Tukey method. Finally, for the spectral analysis of data generated by the chaotic process, the periodogram method does not perform well, whereas, the WOSA and Blackman-Tukey methods give equivalently good results.

Vanel, Florence O.↗

NASA NTRS1998

Ma'adim Vallis Estuarine Delta in Elysium Basin and Its Relevance as a Landing Site for Exobiology Exploration on Mars

The debouche of Ma'adim Vallis in the Elysium Basin generated a transitional transported sediment structure, which planimetric shape is controlled by the enclosing topography of a deep reentrant gulf of the Basin into the highland. We defined it as an estuarine delta. The location and the importance of this estuarine delta is supported by the theoretical model of graded profile constructed for Ma'adim Vallis, and by two approaches: (i) the reconstruction of Ma'adim Vallis downstream course from Gusev to Elysium Basin, and (ii) the survey of the sediment deposit in the alleged estuary. The longitudinal graded profile of Ma'adim Vallis finds its base-level in the Elysium Basin, at a about 1000 m elevation, which is in agreement with the observed Basin shoreline. This model is supported by observational evidence of flow between the northern rim of Gusev crater, and the Elysium Basin shoreline. This downstream course of Ma'adim Vallis can be divided into three hydrogeologic regions. into three hydrogeologic regions. (a) The first region is a flooded plain (Zephiria Mensae), consisting in chaotic terrain formed by highland rocks, and disintegrated lava of the western flank of Apollinaris. Morphologic indicators of the flood process are: (1) the sediment deposit over the Gusev crater northern rim that reflects the overspilling of the crater-lake water through a 40-km wide gap provided by an ancient impact crater, (2) the tear-drop shaped feature on the northeastern flank of Apollinaris Patera, and (3) the chaotic terrain that suggest the emergence of ground water generated by the seepage of the crater lake through high-permeable broken rampart material. This underground water circulation sustained by the hydrostatic pressure of the crater-lake has likely generated a hydrothermal system in the volcanic environment of Apollinaris Patera. The stratigraphy of the flooded area is identified as Hesperian age, with occurrences of Noachian hilly individual features, and as Amazonian flooded plain and chaotic material, (b) The second region is located on the western flank of Apollinaris Patera. It is surrounded by relics of deep valleys that suggest a former downstream course of Ma'adim Vallis. The geologic setting of this region (Lucus Planum) is interpreted to be an Amazonian formation composed by the middle and lower members of the Medusae Formation., c) The third region corresponds to the convergence of the west and east branches of Ma'adirn Vallis into a deep re-entrant wide gulf that penetrates about 100 km into the highland. This topographic depression is delineated by the 1000 in elevation contour. This gulf has formed an estuarine configuration centered at 3S/190W within the Elysium Basin. This configuration has favored the formation of a estuarine sedimentary delta, because of topographically controlled lateral migration. This estuarine structure is strongly dominated by the incoming supply of Ma'adim Vallis fluvial sediment extracted from Zephiria Mensae and Lucus Planum. The obtuse-angle geometry of the estuary increases the sedimentation rate, which is higher than in the course of the channel. The sediment deposition process is governed by the estuarine water circulation. The inflowing loaded fluvial water enters the estuary as a bottom current, and mixes with the relatively less-loaded water of the receiving basin. When they mixed. the inflowing fluvial material, and the landward basin circulating water generate an accumulation of highly-diversified estuarine deposit stratification. This accumulation of material is mostly centered in the transitional zone of the delta. The sediment trapping efficiency of the estuary is function of the energy balance between the inflowing fluvial water, and the ingoing basin current. The submergence of the delta by the rising of the water-level increases the estuary water-depth, and consequently the sediment entrapment is favored. The locus of sediment accumulation moves landward in the zone of inflowing fluvial water. This results in the rising of the channel base-level, thus in the increase of the length of the longitudinal graded-profile. The sediment deposit facies of the zone A shows a generally smooth surface. The longitudinal deposit is bordered by alluvial terraces that reflect the variations of the channel level. The waning of the Elysium Basin caused the erosion of the Basin estuarine zone by small channels, this episode being characterized by dissected tear-drop shaped mesa-like morphologies in the delta. Our estuarine delta model predicts a lithostratigraphic depositional sequence associated with the water submergence and the transgression of Elysium Basin. The thickness of the estuarine sediment corresponds to the Elysium Basin levels changes relatively to the bed floor of the estuary, The depositional sequence of Ma'adim Vallis are described: (1) a pro-current filled region (A), where fluvial are longitudinally accumulated by the inflowing water, (2) inverse current from Elysium Basin (B), where fluvial and lacustrine sediments are accumulated, and (3) zone of current equilibrium (C), where the sediments are distributed as a shoreline at the boundary of the estuarine delta. The estuary sedimentology dynamics collects and keeps the record of the geologic unit material crossed by Ma'adim Vallis, and those of the lakebed deposit of Elysium Basin. The predicted mixed stratigraphic sequence from fluvial and lacustrine sediment makes this site an exceptional environment to concentrate potential multi-origin biologic records. We envision four possible strategies to explore this sedimentologic record: (1) longitudinal surface and subsurface traverses in region A to investigate outcrop levees, (2) exploration of the mesa walls in region B, (3) deep drilling hole lodging of the sequential deposits in the zones A and B, and (4) surface and subsurface exploration of the shoreline delta. The expected results for each of these strategies are: (1) in the deepest layers of region A are predicted frequent and abundant coarse material, sandy lenses lamination grading downward from sand to cobbles. Volcanic debris from the Noachian crustal Plateau unit material, hydrothermal altered rocks, carbonates, Hesperian and possibly Amazonian volcanic material, from Apollinaris Patera, altered rocks and carbonates from Zephiria Mensae are expected. As a favorable environment for inception of life, possible biological records are expected in transported rock, (2) At the surface, and subsurface (<=100 m), large deposits sandy to silted material from Elysium paleolake basin mixed with fine-grained sediments from Ma'adim Vallis are expected mostly in the upstream part of region B, (3) on the shoreline of the estuarine delta, abundant fine material from Elysium paleolake basin (evaporites, carbonates), mostly Amazonian in age are expected. The Ma'adini estuary is a favorable landing site for all the above mentioned science aspects, and .for its location. The site lies near the equator, which is favorable for the rover solar power supply, and at 1000m elevation, which is a favorable configuration for the descent system braking. Another advantage is the extent of the area of high scientific interest (33,000 sq km), which provides a good ellipse, and potential long study traverses.

Grin, E. A.↗