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In this paper we consider microphysical processes which affect the formation of sulfate particles and their size distribution in a dispersing cloud. A model for the dispersion of the Mt. Pinatubo volcanic cloud is described. We then consider a single point in the dispersing cloud and study the effects of nucleation, condensation and coagulation on the time evolution of the particle size distribution at that point.
The direct-beam spectral extinction of solar radiation contains information on atmospheric composition in a form that is essentially free from the data analysis complexities that often arise from multiple scattering. Ground based Multi-Filter Shadowband Radiometer (MFRSR) measurements provide such information for the vertical atmospheric column path, while solar occultation measurements from a satellite platform provide horizontal slices through the atmosphere. We describe application of a Multi-Spectral Atmospheric Column Extinction (MACE) analysis technique used to analyze MFRSR data also to occultation measurements made by SAGE 11. For analysis, we select the 1985 Nevado del Ruiz volcanic eruption period to retrieve atmospheric profiles of ozone and NO2, and changes in the stratospheric aerosol size and optical depth. The time evolution of volcanic aerosol serves as a passive tracer to study stratospheric dynamics, and changes in particle size put constraints on the sulfur chemistry modeling of volcanic aerosols.
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.
The process of generating a block-structured mesh with the smoothness required for high-accuracy schemes is still a time-consuming process often measured in weeks or months. Unstructured grids about complex geometries are more easily generated, and for this reason, methods using unstructured grids have gained favor for aerodynamic analyses. The discontinuous Galerkin (DG) method is a compact finite-element projection method that provides a practical framework for the development of a high-order method using unstructured grids. Higher-order accuracy is obtained by representing the solution as a high-degree polynomial whose time evolution is governed by a local Galerkin projection. The traditional implementation of the discontinuous Galerkin uses quadrature for the evaluation of the integral projections and is prohibitively expensive. Atkins and Shu introduced the quadrature-free formulation in which the integrals are evaluated a-priori and exactly for a similarity element. The approach has been demonstrated to possess the accuracy required for acoustics even in cases where the grid is not smooth. Other issues such as boundary conditions and the treatment of non-linear fluxes have also been studied in earlier work This paper describes the application of the quadrature-free discontinuous Galerkin method to a two-dimensional shear layer problem. First, a brief description of the method is given. Next, the problem is described and the solution is presented. Finally, the resources required to perform the calculations are given.
Observations indicate that the Earth was at least warm enough for liquid water to exist as far back as 4 Gyr ago, namely, as early as half a billion years after the formation of the Earth; in fact, there is evidence suggesting that Earth may have been even warmer then than it is now. These relatively warm temperatures required on early Earth are in apparent contradiction to the dimness of the early Sun predicted by the standard solar models. This problem has generally been explained by assuming that Earth's early atmosphere contained huge amounts of carbon dioxide (CO2), resulting in a large enough greenhouse effect to counteract the effect of a dimmer Sun. However, recent work places an upper limit of 0.04 bar on the partial pressure of CO2 in the period from 2.75 to 2.2 Gyr ago, based on the absence of siderite in paleosols; this casts doubt on the viability of a strong CO2 greenhouse effect on early Earth. The existence of liquid water on early Mars has been even more of a puzzle; even the maximum possible CO2 greenhouse effect cannot yield warm enough Martian surface temperatures. These problems can be resolved simultaneously for both Earth and Mars, if the early Sun was brighter than predicted by the standard solar models. This could be accomplished if the early Sun was slightly more massive than it is now, i.e., if the solar wind was considerably stronger in the past than at present. A slightly more massive young Sun would have left fingerprints on the internal structure of the present Sun. Today, helioseismic observations exist that can measure the internal structure of the Sun with very high precision. The task undertaken here was to compute solar models with the highest precision possible at this time, starting with slightly greater initial masses. These were evolved to the present solar age, where comparisons with the helioseismic observations could be made. Our computations also yielded the time evolution of the solar flux at the planets - a key input to the climates of early Earth and Mars. Early solar mass loss is not the only influence that can alter the internal structure of the present Sun. There are minor uncertainties in the physics of the solar models and in the key observed solar parameters that also affect the present Sun's internal structure. It was therefore imperative to obtain an understanding of the effects of these other uncertainties, in order to disentangle them from the fingerprints that might be left by early solar mass loss. From these considerations, our work was divided into two parts: (1) We first computed the evolution of standard solar models with input parameters varied within their uncertainties, to determine their effect on the observable helioseismic quantities; (2) We then computed non-standard solar models with higher initial masses to test against the helioseismological observations.
It is widely recognized that the structure and complexity of compressible fluid flow places high demands on numerical discretization techniques for the fluid flow equations. Fluid flows arising in external aerodynamics often contain both flow field discontinuities and fluid boundary-layers. Both must be accurately resolved to provide useful information to aerodynamic design and analysis engineers. These accuracy requirements motivated the present author to examine a class of finite-volume techniques on arbitrary triangulated domains based on linear or quadratic reconstruction of integral-averaged data followed by upwind flux function evaluation and small time evolution. More recently, we have considered some new upwind techniques which yield compact discretizations while maintaining higher order accuracy. In the mini-symposium talk we will discuss both of these techniques as well as demonstrate the relative merits of each method by computing a number of aerodynamic flows containing shock waves and boundary-layers.
An approximation to the Maxwell-Semiconductor Bloch equations is solved for the transverse modes of vertical-cavity surface-emitting lasers. A finite-difference algorithm will be used to calculate the detailed time evolution of the transverse mode profiles of VCSELs. Effects of pumping current and refractive index profiles will be investigated.
The surface heat budgets, sea surface temperature (SST), clouds and winds in the tropical western Pacific are analyzed and compared for the periods April-June 1998 and 1999. The spring of 1998 is in the later phase of a strong El Nino, whereas the spring of 1999 is in a period of a La Nina. The surface shortwave (SW) and longwave (LW) radiative fluxes are retrieved from Japanese Geostationary Meteorological Satellite radiance measurements, while the surface turbulent fluxes (latent and sensible heat) are derived from SSM/I-Inferred surface air humidity and winds. The SST and sea-air temperature differences are taken from NCEP/NCAR reanalysis. Deep convection is inferred from the outgoing longwave radiation of NOAA's polar-orbiting satellites. The longitudinal shift in maximum SST, deep convection and winds during El Nino and La Nina have a large impact on the spatial distribution of surface heating. Changes in clouds between these two periods have a large impact on the monthly-mean radiative heating, exceeding 60 W m(exp -2) over large oceanic regions. Similarly, the differences in wind speeds and SST have a large impact on the latent cooling, exceeding 40 W m(exp -2) over large oceanic areas. However, the maximum impacts on radiative and latent heat fluxes occur in different regions. The regions of maximum impact on radiative fluxes coincide with the regions of maximum change in clouds, whereas regions of maximum impact on turbulent heat fluxes coincide with the regions of maximum change in trade winds. The time-evolution of SST in relation to that of surface heat fluxes and winds are investigated and compared between the two El Nino and La Nina periods. In regions where wind speeds (or wind stresses) are large, the change in SST agrees well with the change in the net surface heating, indicating a deep ocean mixed layer associated with strong trade winds. On the other hand, in regions where radiative fluxes are large, the change in SST does not agree well with the change in the net surface heating, indicating the importance of solar radiation penetrating through the bottom of the shadow ocean mixed layer.
We have constructed an optical system for observing the internal structure of freely suspended smectic liquid crystal bubbles using a reflected light microscope. Liquid crystal bubbles can have thicker circular regions (islands) which can easily be generated by shrinking the bubble diameter. The diameter of these islands is approximately 10 microns and they are typically up to five times thicker than the surrounding liquid crystal film (500 angstroms). In the Laboratory, the location of the islands is strongly influenced by gravity, which causes the majority of islands to migrate to the bottom half of the bubble. We will describe the size and thickness distributions of islands and their time evolution, and also discuss two-dimensional hydrodynamics and turbulence of smectic bubbles, the shapes of islands and holes affected by bubble vibrations, and the interactions between islands, which we have probed using optical tweezers.
Compressor stall is a catastrophic breakdown of the flow in a compressor, which con lead to a loss of engine power, large pressure transients in the inlet/nacelle, and engine flameout. The implementation of active or passive strategies for controlling rotating stall and surge can significantly extend the stable operating range of a compressor without substantially sacrificing performance. It is crucial to identify the dynamic changes occurring in the flow field prior to rotating stall and surge in order to control these events successfully. Generally, pressure transducer measurements are made to capture the transient response of a compressor prior to rotating stall. In this investigation, Digital Particle Imaging Velocimetry (DPIV) is used in conjunction with dynamic pressure transducers to capture transient velocity and pressure measurements simultaneously in the nonstationary flow field during compressor surge. DPIV is an instantaneous, planar measurement technique that is ideally suited for studying transient flow phenomena in highspeed turbomachinery and has been used previously to map the stable operating point flow field in the diffuser of a high-speed centrifugal compressor. Through the acquisition of both DPIV images and transient pressure data, the time evolution of the unsteady flow during surge is revealed.
Compressor stall is a catastrophic breakdown of the flow in a compressor, which can lead to a loss of engine power, large pressure transients in the inlet/nacelle and engine flameout. The implementation of active or passive strategies for controlling rotating stall and surge can significantly extend the stable operating range of a compressor without substantially sacrificing performance. It is crucial to identify the dynamic changes occurring in the flow field prior to rotating stall and surge in order to successfully control these events. Generally, pressure transducer measurements are made to capture the transient response of a compressor prior to rotating stall. In this investigation, Digital Particle Imaging Velocimetry (DPIV) is used in conjunction with dynamic pressure transducers to simultaneously capture transient velocity and pressure measurements in the non-stationary flow field during compressor surge. DPIV is an instantaneous, planar measurement technique which is ideally suited for studying transient flow phenomena in high speed turbomachinery and has been used previously to successfully map the stable operating point flow field in the diffuser of a high speed centrifugal compressor. Through the acquisition of both DPIV images and transient pressure data, the time evolution of the unsteady flow during surge is revealed.
The MHD equations are a system of non-strictly hyperbolic conservation laws. The non-convexity of the inviscid flux vector resulted in corresponding Jacobian matrices with undesirable properties. It has previously been shown by Powell et al. (1995) that an 'almost' equivalent MHD system in non-conservative form can be derived. This non-conservative system has a better conditioned eigensystem. Aside from Powell et al., the MHD equations can be derived from basic principles in either conservative or non-conservative form. The Delta x B = 0 constraint of the MHD equations is only an initial condition constraint, it is very different from the incompressible Navier-Stokes equations in which the divergence condition is needed to close the system (i.e., to have the same number of equations and the same number of unknown). In the MHD formulations, if Delta x B = 0 initially, all one needs is to construct appropriate numerical schemes that preserve this constraint at later time evolutions. In other words, one does not need the Delta x B condition to close the MHD system. We formulate our new scheme together with the Cargo & Gallice (1997) form of the MHD approximate Riemann solver in curvilinear grids for both versions of the MHD equations. A novel feature of our new method is that the well-conditioned eigen-decomposition of the non-conservative MHD equations is used to solve the conservative equations. This new feature of the method provides well-conditioned eigenvectors for the conservative formulation, so that correct wave speeds for discontinuities are assured. The justification for using the non-conservative eigen-decomposition to solve the conservative equations is that our scheme has a better control of the numerical error associated with the divergence of the magnetic condition. Consequently, computing both forms of the equations with the same eigen-decomposition is almost equivalent. It will be shown that this approach, using the non-conservative eigensystem when solving the conservative equations, also works well in the context of standard shock-capturing schemes.
One of the most promising methods to test the representation of cloud processes used in climate models is to use observations together with Cloud Resolving Models (CRMs). The CRMs use more sophisticated and realistic representations of cloud microphysical processes, and they can reasonably well resolve the time evolution, structure, and life cycles of clouds and cloud systems (size about 2-200 km). The CRMs also allow explicit interaction between out-going longwave (cooling) and in-coming solar (heating) radiation with clouds. Observations can provide the initial conditions and validation for CRM results. The Goddard Cumulus Ensemble (GCE) Model, a CRM, has been developed and improved at NASA/Goddard Space Flight Center over the past two decades. The GCE model has been used to understand the following: 1) water and energy cycles and their roles in the tropical climate system; 2) the vertical redistribution of ozone and trace constituents by individual clouds and well organized convective systems over various spatial scales; 3) the relationship between the vertical distribution of latent heating (phase change of water) and the large-scale (pre-storm) environment; 4) the validity of assumptions used in the representation of cloud processes in climate and global circulation models; and 5) the representation of cloud microphysical processes and their interaction with radiative forcing over tropical and midlatitude regions. Four-dimensional cloud and latent heating fields simulated from the GCE model have been provided to the TRMM Science Data and Information System (TSDIS) to develop and improve algorithms for retrieving rainfall and latent heating rates for TRMM and the NASA Earth Observing System (EOS). More than 90 referred papers using the GCE model have been published in the last two decades. Also, more than 10 national and international universities are currently using the GCE model for research and teaching. In this talk, five specific major GCE improvements: (1) ice microphysics, (2) longwave and shortwave radiative transfer processes, (3) land surface processes, (4) ocean surface fluxes and (5) ocean mixed layer processes are presented. The performance of these new GCE improvements will be examined. Observations are used for model validation.
Shock acceleration is an ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., the Buneman instability, two-streaming instability, and the Weibel instability) created in the shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic jet front propagating through an ambient plasma with and without initial magnetic fields. We find only small differences in the results between no ambient and weak ambient magnetic fields. Simulations show that the Weibel instability created in the collisionless shock front accelerates particles perpendicular and parallel to the jet propagation direction. The simulation results show that this instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields, which contribute to the electron s transverse deflection behind the jet head. The jitter radiation (Medvedev 2000) from deflected electrons has different properties than synchrotron radiation which is calculated in a uniform magnetic field. This jitter radiation may be important to understanding the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets, and supernova remnants.
Shock wave acceleration is an ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., the Buneman instability, two-streaming instability, and the Weibel instability) created in the shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic jet front propagating through an ambient plasma with and without initial magnetic fields. We find only small differences in the results between no ambient and weak ambient magnetic fields. Simulations show that the Weibel instability created in the collisionless shock front accelerates particles perpendicular and parallel to the jet propagation direction. While some Fermi acceleration may occur at the jet front, the majority of electron acceleration takes place behind the jet front and cannot be characterized as Fermi acceleration. The simulation results show that this instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields, which contribute to the electron's transverse deflection behind the jet head. The 'jitter' radiation from deflected electrons has different properties than synchrotron radiation which is calculated in a uniform magnetic field. This jitter radiation may be important to understanding the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets, and supernova remnants.
Shock acceleration is an ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., the Buneman instability, two-streaming instability, and the Weibel instability) created in the shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic jet front propagating through an ambient plasma with and without initial magnetic fields. We find only small differences in the results between no ambient and weak ambient magnetic fields. Simulations show that the Weibel instability created in the collisionless shock front accelerates particles perpendicular and parallel to the jet propagation direction. While some Fermi acceleration may occur at the jet front, the majority of electron acceleration takes place behind the jet front and cannot be characterized as Fermi acceleration. The simulation results show that this instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields, which contribute to the electron s transverse deflection behind the jet head. The "jitter" radiation from deflected electrons has different properties than synchrotron radiation which is calculated in a uniform magnetic field. This jitter radiation may be important to understanding the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets, and supernova remnants.
One of the most promising methods to test the representation of cloud processes used in climate models is to use observations together with Cloud Resolving Models (CRMs). The CRMs use more sophisticated and realistic representations of cloud microphysical processes, and they can reasonably well resolve the time evolution, structure, and life cycles of clouds and cloud systems (size about 2-200 km). The CRMs also allow explicit interaction between out-going longwave (cooling) and incoming solar (heating) radiation with clouds. Observations can provide the initial conditions and validation for CRM results. The Goddard Cumulus Ensemble (GCE) Model, a cloud-resolving model, has been developed and improved at NASA/Goddard Space Flight Center over the past two decades. Dr. Joanne Simpson played a central role in GCE modeling developments and applications. She was the lead author or co-author on more than forty GCE modeling papers. In this paper, a brief discussion and review of the application of the GCE model to (1) cloud interactions and mergers, (2) convective and stratiform interaction, (3) mechanisms of cloud-radiation interaction, (4) latent heating profiles and TRMM, and (5) responses of cloud systems to large-scale processes are provided. Comparisons between the GCE model's results, other cloud-resolving model results and observations are also examined.
We observe two near-limb solar filament eruptions, one of 2000 February 26 and the other of 2002 January 4. For both we use 195 Angstroms Fe XII images from the Extreme-Ultraviolet (EUV) Imaging Telescope (EIT) and magnetograms from the Michelson Doppler Imager (MDI), both on the Solar and Heliospheric Observatory (SOHO) satellite. For the earlier event we also use soft X-ray telescope (SXT), hard X-ray telescope (HXT), and Bragg Crystal Spectrometer (BCS) data from the Yohkoh satellite, and hard X-ray data from the BATSE experiment on the Compton Gamma Ray Observatory (CGRO). Both events occur in quadrupolar magnetic regions, and both have coronal features that we infer belong to the same magnetic-cavity structures as the filaments. In both cases the cavity and filament first rise slowly at approximately 10 kilometers per second prior to eruption, and then accelerate to approximately 100 kilometers per second during the eruption, although the slow-rise movement for the higher-altitude cavity elements is clearer in the later event. We estimate both filaments and both cavities to contain masses of approximately 10(exp 14-15) g and approximately 10(exp 15-16) g respectively. We consider whether two specific magnetic-reconnection-based models for eruption onset, the tether cutting and the breakout models, are consistent with our observations. In the earlier event soft X-rays from SXT show an intensity increase during the 12-minute interval over whch fast eruption begins, which is consistent with tether-cutting-model predictions. Substantial hard X-rays, however, do not occur until after fast eruption is underway, and so this is a constraint the tether-cutting model must satisfy. During the same 12-minute interval over which fast eruption begins, there are brightenings and topological changes in the corona indicative of high-altitude reconnection early in the eruption, and this is consistent with breakout predictions. In both eruptions, however, the onset of the filament fast-rise phase occurs while overlying cavity-related coronal loops are still evolving from a "closed" state to an "open" state, and our observations of the time evolution of these loops compared to the eruption state in both events are constraints the breakout model must meet. Therefore our findings are consistent with runaway-tether-cutting-type reconnection and fast breakout-type reconnection both occurring early in the fast phase of the February eruption and with both types of reconnection being important in unleashing the explosion, but we are not able to say which, if either, type of reconnection actually triggered the fast phase. We have also found specific constraints that either model, or any other model, must satisfy if correct.