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NASA NTRS1995

Property-Based Software Engineering Measurement

Little theory exists in the field of software system measurement. Concepts such as complexity, coupling, cohesion or even size are very often subject to interpretation and appear to have inconsistent definitions in the literature. As a consequence, there is little guidance provided to the analyst attempting to define proper measures for specific problems. Many controversies in the literature are simply misunderstandings and stem from the fact that some people talk about different measurement concepts under the same label (complexity is the most common case). There is a need to define unambiguously the most important measurement concepts used in the measurement of software products. One way of doing so is to define precisely what mathematical properties characterize these concepts regardless of the specific software artifacts to which these concepts are applied. Such a mathematical framework could generate a consensus in the software engineering community and provide a means for better communication among researchers, better guidelines for analysis, and better evaluation methods for commercial static analyzers for practitioners. In this paper, we propose a mathematical framework which is generic, because it is not specific to any particular software artifact, and rigorous, because it is based on precise mathematical concepts. This framework defines several important measurement concepts (size, length, complexity, cohesion, coupling). It is not intended to be complete or fully objective; other frameworks could have been proposed and different choices could have been made. However, we believe that the formalism and properties we introduce are convenient and intuitive. In addition, we have reviewed the literature on this subject and compared it with our work. This framework contributes constructively to a firmer theoretical ground of software measurement.

Briand, Lionel↗
NASA NTRS1998

GCM Studies on the Interactions Between Photosynthesis and Climate at Diurnal to Decadal Time Scales

Transpiration, a major component of total evaporation from vegetated surfaces, is an unavoidable consequence of photosynthetic carbon fixation. Because of limiting soil moisture and competition for solar radiation plants invest most of their fixed carbon into structural and hydraulic functions (roots and stems) and solar radiation absorption (leaves). These investments permit individuals to overshadow competitors and provide for transport of water from the soil to the leaves where photosynthesis and transpiration occur. Often low soil moisture or high evaporative demand limit the supply of water to leaves reducing photosynthesis and thus transpiration. The absorption of solar radiation for photosynthesis and dissipation of this energy via radiation, heat, mass and momentum fluxes represents the link between photosynthesis and climate. Recognition of these relationships has led to the development of hydro/energy balance models that are based on the physiological ecology of photosynthesis. We discuss an approach to study vegetation-climate interactions using photosynthesis-centric models embedded in a GCM. The rate at which a vegetated area transpires and photosynthesizes is determined by the physiological state of the vegetation, its amount and its type. The latter two are specified from global satellite data collected since 1982. Climate simulations have been carried out to study how this simulated climate system responds to changes in radiative forcing, physiological capacity, atmospheric CO2, vegetation type and variable vegetation cover observed from satellites during the 1980's. Results from these studies reveal significant feedbacks between the vegetation activity and climate. For example, vegetation cover and physiological activity increases cause the total latent heat flux and precipitation to increase while mean and maximum air temperatures decrease. The reverse occurs if cover or activity'decreases. In general climate response of a particular region was dominated by local processes but we also find evidence that plausible climate-vegetation scenarios lead to changes in global atmospheric circulation and strong non-local influences in some cases.

Collatz, G. James↗
NASA NTRS1997

Property-Based Software Engineering Measurement

Little theory exists in the field of software system measurement. Concepts such as complexity, coupling, cohesion or even size are very often subject to interpretation and appear to have inconsistent definitions in the literature. As a consequence, there is little guidance provided to the analyst attempting to define proper measures for specific problems. Many controversies in the literature are simply misunderstandings and stem from the fact that some people talk about different measurement concepts under the same label (complexity is the most common case). There is a need to define unambiguously the most important measurement concepts used in the measurement of software products. One way of doing so is to define precisely what mathematical properties characterize these concepts, regardless of the specific software artifacts to which these concepts are applied. Such a mathematical framework could generate a consensus in the software engineering community and provide a means for better communication among researchers, better guidelines for analysts, and better evaluation methods for commercial static analyzers for practitioners. In this paper, we propose a mathematical framework which is generic, because it is not specific to any particular software artifact and rigorous, because it is based on precise mathematical concepts. We use this framework to propose definitions of several important measurement concepts (size, length, complexity, cohesion, coupling). It does not intend to be complete or fully objective; other frameworks could have been proposed and different choices could have been made. However, we believe that the formalisms and properties we introduce are convenient and intuitive. This framework contributes constructively to a firmer theoretical ground of software measurement.

Briand, Lionel C.↗
NASA NTRS1998

Re-Evaluation of the Role of Starch in Gravitropic Sensing

Plant organs grow toward or away from gravity as a way to orient those organs for optimizing growth. Starch has long been thought to be important in sensing the direction of the g-vector in gravitropism, but that hypothesis has also evoked controversy. We have previously shown that starch-deficient mutants of Arabidopsis (TC7) and Nicotiana (NS458) are impaired in their gravitropism. While this suggests that starch is not necessary for reduced gravitropism, it also indicates that the mass of the starch contributes to sensing when present and thus is necessary for full gravitropic sensitivity. The research supported by this grant focused on three related projects, (1) the effect of light on hypocotyl gravitropism in NS458, (2) the effects of root phototropism on measurements of gravitropic sensitivity, and (3) the effects of starch overproduction on sedimentation and gravitropism. Collectively, our results provide additional strong support for the importance of starch in gravitropic sensing. First, by accounting for negative phototropism in roots of two starchless mutants of Arabidopsis we have established that these mutants are much less sensitive to gravity than previously thought. This work also demonstrates the importance of designing experimental protocols that remove the influence of root phototropism on measuring root gravitropism. Second, light apparently promotes gravitropism in starch-deficient Nicotiana hypocotyls by increasing the trace amounts of starch in the plastids, by inducing limited plastid sedimentation and thus by presumably increasing the signal provided by plastid mass. And finally, we show that excess starch in Arabidopsis seedlings has little effect on gravitropic sensitivity implying that the sensing system is already saturated. However, in light-grown stems where this mutation results in starch accumulation and where the wild-type practically lacks starch in the sensing cells, the mutant is much more sensitive than the wild-type again showing that the loss of starch depresses gravity sensing.

Sack, Fred D.↗
NASA NTRS1999

NASA University Program Management Information System

As basic policy, NASA believes that colleges and universities should be encouraged to participate in the nation's space and aeronautics program to the maximum extent practicable. Indeed, universities are considered as partners with government and industry in the nation's aerospace program. NASA's objective is to have them bring their scientific, engineering, and social research competence to bear on aerospace problems and on the broader social, economic, and international implications of NASA's technical and scientific programs. It is expected that, in so doing, universities will strengthen both their research and their educational capabilities to contribute more effectively to the national well-being. NASA field codes and certain Headquarters program offices provide funds for those activities in universities which contribute to the mission needs of that particular NASA element. Although NASA has no predetermined amount of money to devote to university activities, the effort funded each year is substantial. (See the bar chart on the next page). This annual report is one means of documenting the NASA-university relationship, frequently denoted, collectively, as NASA's University Program. This report is consistent with agency accounting records, as the data is obtained from NASA's Financial and Contractual Status (FACS) System, operated by the Financial Management Division and the Procurement Office. However, in accordance with interagency agreements, the orientation differs from that required for financial or procurement purposes. Any apparent discrepancies between this report and other NASA procurement or financial reports stem from the selection criteria for the data.

Source record↗
NASA NTRS1999

Fundamental Studies of Solidification in Microgravity Using Real-Time X-Ray Microscopy

This research applies a state of the art X-ray Transmission Microscope, XTM, to image (with resolutions up to 3 micrometers) the solidification of metallic or semiconductor alloys in real-time. We have successfully imaged in real-time: interfacial morphologies, phase growth, coalescence, incorporation of phases into the growing interface, and the solute boundary layer in the liquid at the solid-liquid interface. We have also measured true local growth rates and can evaluate segregation structures in the solid; a form of in-situ metallography. During this study, the growth of secondary phase fibers and lamellae from eutectic and monotectic alloys have been imaged during solidification, in real-time, for the first time in bulk metal alloys. Current high resolution X-ray sources and high contrast X-ray detectors have advanced to allow systematic study of solidification dynamics and the resulting microstructure. We have employed a state-of-the-art sub-micron source with acceleration voltages of 10-100 kV to image solidification of metals. One useful strength of the XTM stems from the manner an image is formed. The radiographic image is a shadow formed by x-ray photons that are not absorbed as they pass through the specimen. Composition gradients within the specimen cause variations in absorption of the flux such that the final image represents a spatial integral of composition (or thickness). The ability to image these features in real-time enables more fundamental and detailed understanding of solidification dynamics than has previously been possible. Hence, application of this technique towards microgravity experiments will allow rigorous testing of critical solidification models.

Curreri, Peter A.↗
NASA NTRS1998

Protein Crystallization: Specific Phenomena and General Insights on Crystallization Kinetics

Experimental and simulation studies of the nucleation and growth kinetics of proteins have revealed phenomena that are specific for macromolecular crystallization, and others that provide a more detailed understanding of solution crystallization in general. The more specific phenomena, which include metastable liquid-liquid phase separations and gelation prior to solid nucleation, are due to the small ratio of the intermolecular interaction-range to the size of molecules involved. The apparently more generally applicable mechanisms include the cascade-like formation of macrosteps, as an intrinsic morphological instability that roots in the coupled bulk transport and nonlinear interface kinetics in systems with mixed growth rate control. Analyses of this nonlinear response provide (a) criteria for the choice of bulk transport conditions to minimize structural defect formation, and (b) indications that the "slow" protein crystallization kinetics stems from the mutual retardation of growth steps.

Rosenberger, F.↗
NASA NTRS1999

A Study of Flame Propagation on Water-Mist Laden Gas Mixtures in Microgravity

The use of water mists (very fine water sprays) for fire suppression is currently receiving increased attention as a replacement technology for halogen-based chemical agents-such as Halon 1301 (CF3Br)--the manufacturing of which has been banned by the Montreal Protocol due to their high ozone depletion potential. Water mist technology has been found effective for a wide range of applications such as Class B pool fires, shipboard machinery, aircraft cabins, computers, and electronic equipment. There are five distinct mechanisms by which water droplets may interact with a flame. First, the high enthalpy of vaporization of water (2450 kJ/kg) leads to heat removal from the flame front as the liquid droplets turn to steam. Second, as water vaporizes its volume increases approximately three orders of magnitude, which leads to the dilution of the oxygen and vaporized fuel required to maintain the flame. The third effect is the recombination of H-atoms and other radicals on the droplet surface. A fourth effect of water mists in fires is the retardation of surface propagation rates due to the wetting of walls and surfaces. The last potential impact of fine water mists affects the radiative propagation of the fire by forming an optically thick barrier to infrared radiation which prevents ignition of the unburned regions. Unfortunately, little fundamental information exists on the interaction of a flame with a water mist. To date, there is no widely accepted interpretation of the critical concentration of droplets required to suppress a flame or of the fundamental mechanisms involved in flame extinguishment by water mists. One of the main obstacles to obtaining such understanding is the difficulty of providing a simple, well-defined experimental setup for the flame front/water mist interaction. Some of the difficulty stems from the problem of generating, distributing and maintaining a homogeneous concentration of droplets throughout a chamber while gravity depletes the concentration and alters the droplet size by coalescence and agglomeration mechanisms. Experiments conducted in the absence of gravity provide an ideal environment to study the interaction of water mists and flames by eliminating these distorting effects. In addition, microgravity eliminates the complex flow patterns induced between the flame front and the water droplets. The long duration and quality of microgravity in space flights provide the required conditions to perform the setup and monitoring of flame suppression experiments. Consequently, a series of experiments have been identified to be performed on the Combustion Module (CM-2) in the Space Shuttle. These consist of measuring the extinguishing capability of a water mist on a premixed flame propagating along a tube. These experiments should provide the necessary data to obtain further understanding of the water mist suppression phenomena that can be later used to design and manufacture appropriate fire suppression systems. In preparation for the orbital flights, experiments have been conducted on low-gravity ground facilities to obtain the preliminary data necessary to define the scientific objectives and technical issues of the spacecraft experiments.

Abbud-Madrid, A.↗
NASA NTRS1996

1985 Voyager 2 Radio Ranging Measurements of Coronal Density: Asymmetry in the Radial Profiles Explained

An asymmetry in the radial variation of electron density above the cast and west limbs of the Sun was inferred from centimeter wavelength ranging measurements conducted by Voyager 2 during its 1985 solar conjunction. The Voyager 2 ranging measurements, which took place in the heliocentric distance range of 7-40 solar radius, have been compared with the white-light coronagraph measurements of the underlying corona collected by the Mark 3 K-coronameter located at the Mauna Loa Solar Observatory. It is shown that the disparity in radial profiles is not real but is instead caused by longitudinal variations stemming from the probing of significantly different source regions its revealed in the white-light measurements. These results improve our understanding of the probing abilities of ranging measurements and their relationship to white-light measurements. They reinforce the notion that the high-precision and high-sensitivity features of ranging measurements are more fully exploited in the investigation of density variations across the ubiquitous low-contrast raylike structures that permit the corona, rather than in determining radial density profiles.

Woo, Richard↗
NASA NTRS1999

Double Diffusive Convection in Materials Processing

A great number of crystals grown in space are plagued by convective motions which contribute to structural flaws. The character of these instabilities is not well understood but is associated with density variations in the presence of residual gravity (g-jitter). As a specific example, past HgCdTe crystal growth space experiments by Lehoczky and co-workers indicate radial compositional asymmetry in the grown crystals. In the case of HgCdTe the rejected component into the melt upon solidification is HgTe which is denser than the melt. The space grown crystals indicate the presence of three dimensional flow with the heavier HgTe-rich material clearly aligned with the residual gravity (0.55-1.55 micro g) vector. This flow stems from double-diffusive convection, namely, thermal and solutal buoyancy driven flow in the melt. The study of double-diffusive convection is multi-faceted and rather vast. In our investigation, we seek to focus on one specific aspect of this discipline that is of direct relevance to materials processing especially crystal growth, namely, the side ways heating regime. This problem has been widely studied, both experimentally and numerically, in the context of solar ponds wherein the system is characterized by a linear salt (solutal) gradient with an imposed lateral temperature gradient. The induced flow instabilities arise from the wide disparity between the fluid thermal diffusivity and the solute diffusivity. The extension of the analysis to practical crystal growth applications has however not been rigorously made and understood. One subtle but important difference in crystal growth systems is the fact that die system solute gradient is non-linear (typically exponential). Besides, the crystal growth problem has the added complexities of solidification, both lateral and longitudinal thermal gradients and segregation phenomena in systems where binary and ternary compounds are being grown. This paper treats the side ways heating problem alone in a model fluid system. Results from detailed numerical calculations, mainly two dimensional are provided. The interactions between a non-linear solute gradient and an imposed transverse thermal gradient are investigated. The buoyancy effects are treated in the traditional Boussinesq approximation and also in a more complete density formulation to address recent concerns of the first approach especially in simulations of the system response in a reduced gravity environment. Detailed flow, temperature and solute field plots along with heat and mass transfer results are presented in the paper. Implications to practical crystal growth systems as discerned from the modeling results are also explored and reported.

Ramachandra, Narayanan↗
NASA NTRS1998

An Experimental Study of the Effects of A Rotating Magnetic Field on Electrically Conducting Aqueous Solutions

The use of a rotating magnetic field for stirring metallic melts has been a commonly adopted practice for a fairly long period. The elegance of the technique stems from its non-intrusive nature and the intense stirring it can produce in an electrically conducting medium. A further application of the method in recent times has been in the area of crystal growth from melts (e.g. germanium). The latter experiments have been mainly research oriented in order to understand the basic physics of the process and to establish norms for optimizing such a technique for the commercial production of crystals. When adapted for crystal growth applications, the rotating magnetic field is used to induce a slow flow or rotation in the melt which in effect significantly curtails temperature field oscillations in the melt. These oscillations are known to cause dopant striations and thereby inhomogeneities in the grown crystal that essentially degrades the crystal quality. The applied field strength is typically of the order of milli-Teslas with a frequency range between 50-400 Hz. In this investigation, we report findings from experiments that explore the feasibility of applying a rotating magnetic field to aqueous salt solutions, that are characterized by conductivities that are several orders of magnitude smaller than semi-conductor melts. The aim is to study the induced magnetic field and consequently the induced flow in such in application. Detailed flow field description obtained through non-intrusive particle displacement tracking will be reported along with an analytical assessment of the results. It is anticipated that the obtained results will facilitate in establishing a parameter range over which the technique can be applied to obtain a desired flow field distribution. This method can find applicability in the growth of crystals from aqueous solutions and give an experimenter another controllable parameter towards improving the quality of the grown crystal.

Ramachandran Narayanan↗
NASA NTRS1998

Structure of Pseudoknot PK26 Shows 3D Domain Swapping in an RNA

3D domain swapping provides a facile pathway for the evolution of oligomeric proteins and allosteric mechanisms and a means for using monomer-oligomer equilibria to regulate biological activity. The term "3D domain swapping" describes the exchange of identical domains between two protein monomers to create an oligomer. 3D domain swapping has, so far, only been recognized in proteins. In this study, the structure of the pseudoknot PK26 is reported and it is a clear example of 3D domain swapping in RNA. PK26 was chosen for study because RNA pseudoknots are required structures in several biological processes and they arise frequently in in vitro selection experiments directed against protein targets. PK26 specifically inhibits HIV-1 reverse transcriptase with nanomolar affinity. We have now determined the 3.1 A resolution crystal structure of PK26 and find that it forms a 3D domain swapped dimer. PK26 shows extensive base pairing between and within strands. Formation of the dimer requires the linker region between the pseudoknot folds to adopt a unique conformation that allows a base within a helical stem to skip one base in the stacking register. Rearrangement of the linker would permit a monomeric pseudoknot to form. This structure shows how RNA can use 3D domain swapping to build large scale oligomers like the putative hexamer in the packaging RNA of bacteriophage Phi29.

Lietzke, Susan E↗
NASA NTRS1999

Numerical Modeling of Crystal of ZnSe by Physical Vapor Transport - Towards a more Comprehensive Formulations

Crystal growth from the vapor phase has various advantages over melt growth. The main advantage is from a lower processing temperature which makes the process more amenable in instances where the melting temperature of the crystal is high. Other benefits stem from the inherent purification mechanism in the process due to differences in the vapor pressures of the native elements and impurities, and the enhanced interfacial morphological stability during the growth process. Further, the implementation of PVT growth in closed ampoules affords experimental simplicity with minimal needs for complex process control which makes it an ideal candidate for space investigations in systems where gravity tends to have undesirable effects on the growth process. Bulk growth of wide band gap II-VI semiconductors by physical vapor transport has been developed and refined over the past several years at NASA MSFC. Results from a modeling study of PVT crystal growth of ZnSe are reported in this paper. The PVT process is numerically investigated using both two-dimensional and fully three-dimensional formulation of the governing equations and associated boundary conditions. Both the incompressible Boussinesq approximation and the compressible model are tested to determine the influence of gravity on the process and to discern the differences between the two approaches. The influence of a residual gas is included in the models. The results show that both the incompressible and compressible approximations provide comparable results and the presence of a residual gas tends to measurably reduce the mass flux in the system. Detailed flow, thermal and concentration profiles will be provided in the final manuscript along with computed heat and mass transfer rates. Comparisons with the 1-D model will also be provided. The effect of gravity on the process from numerical computations shows subtle effects although experimental evidence from vertically and horizontally grown samples show dramatic evidence of gravitational effects. The shortcomings of the problem formulation will be discussed and a framework will be provided leading up towards a more comprehensive model of PVT systems.

Ramachandran, N.↗
NASA NTRS1993

Guidelines for Design and Analysis of Large, Brittle Spacecraft Components

There were two related parts to this work. The first, conducted at The Aerospace Corporation was to develop and define methods for integrating the statistical theory of brittle strength with conventional finite element stress analysis, and to carry out a limited laboratory test program to illustrate the methods. The second part, separately funded at Aerojet Electronic Systems Division, was to create the finite element postprocessing program for integrating the statistical strength analysis with the structural analysis. The second part was monitored by Capt. Jeff McCann of USAF/SMC, as Special Study No.11, which authorized Aerojet to support Aerospace on this work requested by NASA. This second part is documented in Appendix A. The activity at Aerojet was guided by the Aerospace methods developed in the first part of this work. This joint work of Aerospace and Aerojet stemmed from prior related work for the Defense Support Program (DSP) Program Office, to qualify the DSP sensor main mirror and corrector lens for flight as part of a shuttle payload. These large brittle components of the DSP sensor are provided by Aerojet. This document defines rational methods for addressing the structural integrity and safety of large, brittle, payload components, which have low and variable tensile strength and can suddenly break or shatter. The methods are applicable to the evaluation and validation of such components, which, because of size and configuration restrictions, cannot be validated by direct proof test.

Robinson, E. Y.↗
NASA NTRS1998

Crystal Growth of ZnSe by Physical Vapor Transport: A Modeling Study

Crystal growth from the vapor phase has various advantages over melt growth. The main advantage is from a lower processing temperature which makes the process more amenable in instances where the melting temperature of the crystal is high. Other benefits stem from the inherent purification mechanism in the process due to differences in the vapor pressures of the native elements and impurities, and the enhanced interfacial morphological stability during the growth process. Further, the implementation of Physical Vapor Transport (PVT) growth in closed ampoules affords experimental simplicity with minimal needs for complex process control which makes it an ideal candidate for space investigations in systems where gravity tends to have undesirable effects on the growth process. Bulk growth of wide band gap II-VI semiconductors by physical vapor transport has been developed and refined over the past several years at NASA MSFC. Results from a modeling study of PVT crystal growth of ZnSe arc reported in this paper. The PVI process is numerically investigated using both two-dimensional and fully three-dimensional formulation of the governing equations and associated boundary conditions. Both the incompressible Boussinesq approximation and the compressible model are tested to determine the influence of gravity on the process and to discern the differences between the two approaches. The influence of a residual gas is included in the models. The preliminary results show that both the incompressible and compressible approximations provide comparable results and the presence of a residual gas tends to measurably reduce the mass flux in the system. Detailed flow, thermal and concentration profiles will be provided in the final manuscript along with computed heat and mass transfer rates. Comparisons with the 1-D model will also be provided.

Ramachandran, Narayanan↗
NASA NTRS1999

Mapping Vegetation Structure in Kakadu National Park: An AIRSAR and GIS Application in Conservation

Airborne Synthetic Aperture Radar (AIRSAR) data were used to map vegetation structure in Kakadu National Park Australia as part of the PACRIM project. SAR data were co-registered with Landsat TM, aerial photos, and map data in a geographic information system for a small test area consisting of mangrove, floodplain grasslands, lowland tropical evergreen forest and upland mixed deciduous and evergreen tropical forest near the South Alligator River. Landsat (Thematic Mapper) TM very clearly showed the floristic composition and burn scars from the previous years fires and the AIRSAR data provided a profile of vegetation structure. Extensive field data on vegetation species composition and structure were collected across a series of transects in cooperation with a survey of avifauna in an effort to link the habitat edge structure with bird species responses. A test site was found that contained two types of habitat edges: 1) A structure specific edge - characterized by the appearance of a very strong structural change in the forest canopy occurring in the absence of a substantial turnover in floristics. 2) Floristic edge - a sharp transition in vegetation genetic composition with a mixed set of structural changes. Specific polarization combinations were selected that were highly correlated to a set of desired structural parameters found in the field data. Classification routines were employed to group radar pixels into 3 structural classes based on: the Surface Area to Volume ratio (SA/V) of the stems, the SA/V of the branches, and the leaf area index of the canopy. Separate canopy structure maps were then entered into the GIS and bird responses were observed relative to the classes and their boundaries. Follow-on work will consist of extending this approach to neighboring areas, generating structure maps, predicting bird responses across the edges, and make accuracy assessments.

Imhoff, Marc L.↗
NASA NTRS1999

Microflaring in Low-Lying Core Fields and Extended Coronal Heating in the Quiet Sun

We have previously reported analyses of Yohkoh SXT data examining the relationship between the heating of extended coronal loops (both within and stemming from active regions) and microflaring in core fields lying along neutral lines near their footpoints (J. G. Porter, D. A. Falconer, and R. L. Moore 1998, in Solar Jets and Coronal Plumes, ed. T. Guyenne, ESA SP-421, and references therein). We found a surprisingly poor correlation of intensity variations in the extended loops with individual microflares in the compact heated areas at their feet, despite considerable circumstancial evidence linking the heating processes in these regions. Now, a study of Fe XII image sequences from SOHO EIT show that similar associations of core field structures with the footpoints of very extended coronal features can be found in the quiet Sun. The morphology is consistent with the finding of Wang et al. (1997, ApJ 484, L75) that polar plumes are rooted at sites of mixed polarity in the magnetic network. We find that the upstairs/downstairs intensity variations often follow the trend, identified in the active region observations, of a weak correspondence. Apparently much of the coronal heating in the extended loops is driven by a type of core field magnetic activity that is "cooler" than the events having the coronal signature of microflares, i.e., activity that results in little heating within the core fields themselves. This work was funded by the Solar Physics Branch of NASA's Office of Space Science through the SR&T Program and the SEC Guest Investigator Program.

Porter, Jason G.↗
NASA NTRS1998

Ocean Turbulence V: Mesoscale Modeling in Level Coordinates. The Effect of Random Nature of Density

The main result of this paper is the derivation of a new expression for the tracer subgrid term in level coordinates S(l) to be employed in O-GCM. The novel feature is the proper account of the random nature of the density field which strongly affects the transformation from isopycnal to level coordinates of the variables of interest, velocity and tracer fields, their correlation functions and ultimately the subgrid terms. In deriving our result we made use of measured properties of vertical ocean turbulence. The major new results are: 1) the new subgrid expression is different from that of the heuristic GM model, 2) u++(tracer)=1/2u+(thickness), where u++ and u+ are the tracer and thickness bolus velocities. In previous models, u++ = u+, 2) the subgrid for a tracer tau is not the same as that for the density rho even when one accounts for the obvious absence of a diffusion term in the latter. The difference stems from a new treatment of the stochastic nature of the density, 3) the mesoscale diffusivity enters both locally and non-locally, as the integral over all z's from the bottom of the ocean to the level z.

Canuto, V. M.↗