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NASA NTRS1993

The helical decomposition and the instability assumption

Direct numerical simulations show that the triadic transfer function T(k,p,q) peaks sharply when q (or p) is much smaller than k. The triadic transfer function T(k,p,q) gives the rate of energy input into wave number k from all interactions with modes of wave number p and q, where k, p, q form a triangle. This observation was thought to suggest that energy is cascaded downscale through non-local interactions with local transfer and that there was a strong connection between large and small scales. Both suggestions were in contradiction with the classical Kolmogorov picture of the energy cascade. The helical decomposition was found useful in distinguishing between kinematically independent interactions. That analysis has gone beyond the question of non-local interaction with local transfer. In particular, an assumption about the statistical direction of triadic energy transfer in any kinematically independent interaction was introduced (the instability assumption). That assumption is not necessary for the conclusions about non-local interactions with local transfer recalled above. In the case of turbulence under rapid rotation, the instability assumption leads to the prediction that energy is transferred in spectral space from the poles of the rotation axis toward the equator. The instability assumption is thought to be of general validity for any type of triad interactions (e.g. internal waves). The helical decomposition and the instability assumption offer detailed information about the homogeneous statistical dynamics of the Navier-Stokes equations. The objective was to explore the validity of the instability assumption and to study the contributions of the various types of helical interactions to the energy cascade and the subgrid-scale eddy-viscosity. This was done in the context of spectral closures of the Direct Interaction or Quasi-Normal type.

Waleffe, Fabian A.↗
NASA NTRS1993

Second law analysis of a conventional steam power plant

A numerical investigation of exergy destroyed by operation of a conventional steam power plant is computed via an exergy cascade. An order of magnitude analysis shows that exergy destruction is dominated by combustion and heat transfer across temperature differences inside the boiler, and conversion of energy entering the turbine/generator sets from thermal to electrical. Combustion and heat transfer inside the boiler accounts for 53.83 percent of the total exergy destruction. Converting thermal energy into electrical energy is responsible for 41.34 percent of the total exergy destruction. Heat transfer across the condenser accounts for 2.89 percent of the total exergy destruction. Fluid flow with friction is responsible for 0.50 percent of the total exergy destruction. The boiler feed pump turbine accounts for 0.25 percent of the total exergy destruction. Fluid flow mixing is responsible for 0.23 percent of the total exergy destruction. Other equipment including gland steam condenser, drain cooler, deaerator and heat exchangers are, in the aggregate, responsible for less than one percent of the total exergy destruction. An energy analysis is also given for comparison of exergy cascade to energy cascade. Efficiencies based on both the first law and second law of thermodynamics are calculated for a number of components and for the plant. The results show that high first law efficiency does not mean high second law efficiency. Therefore, the second law analysis has been proven to be a more powerful tool in pinpointing real losses. The procedure used to determine total exergy destruction and second law efficiency can be used in a conceptual design and parametric study to evaluate the performance of other steam power plants and other thermal systems.

Liu, Geng↗
NASA NTRS1995

Unsteady Aerodynamic Models for Turbomachinery Aeroelastic and Aeroacoustic Applications

Theoretical analyses and computer codes are being developed for predicting compressible unsteady inviscid and viscous flows through blade rows of axial-flow turbomachines. Such analyses are needed to determine the impact of unsteady flow phenomena on the structural durability and noise generation characteristics of the blading. The emphasis has been placed on developing analyses based on asymptotic representations of unsteady flow phenomena. Thus, high Reynolds number flows driven by small amplitude unsteady excitations have been considered. The resulting analyses should apply in many practical situations and lead to a better understanding of the relevant flow physics. In addition, they will be efficient computationally, and therefore, appropriate for use in aeroelastic and aeroacoustic design studies. Under the present effort, inviscid interaction and linearized inviscid unsteady flow models have been formulated, and inviscid and viscid prediction capabilities for subsonic steady and unsteady cascade flows have been developed. In this report, we describe the linearized inviscid unsteady analysis, LINFLO, the steady inviscid/viscid interaction analysis, SFLOW-IVI, and the unsteady viscous layer analysis, UNSVIS. These analyses are demonstrated via application to unsteady flows through compressor and turbine cascades that are excited by prescribed vortical and acoustic excitations and by prescribed blade vibrations. Recommendations are also given for the future research needed for extending and improving the foregoing asymptotic analyses, and to meet the goal of providing efficient inviscid/viscid interaction capabilities for subsonic and transonic unsteady cascade flows.

Verdon, Joseph M.↗
NASA NTRS1995

Windowed and Wavelet Analysis of Marine Stratocumulus Cloud Inhomogeneity

To improve radiative transfer calculations for inhomogeneous clouds, a consistent means of modeling inhomogeneity is needed. One current method of modeling cloud inhomogeneity is through the use of fractal parameters. This method is based on the supposition that cloud inhomogeneity over a large range of scales is related. An analysis technique named wavelet analysis provides a means of studying the multiscale nature of cloud inhomogeneity. In this paper, the authors discuss the analysis and modeling of cloud inhomogeneity through the use of wavelet analysis. Wavelet analysis as well as other windowed analysis techniques are used to study liquid water path (LWP) measurements obtained during the marine stratocumulus phase of the First ISCCP (International Satellite Cloud Climatology Project) Regional Experiment. Statistics obtained using analysis windows, which are translated to span the LWP dataset, are used to study the local (small scale) properties of the cloud field as well as their time dependence. The LWP data are transformed onto an orthogonal wavelet basis that represents the data as a number of times series. Each of these time series lies within a frequency band and has a mean frequency that is half the frequency of the previous band. Wavelet analysis combined with translated analysis windows reveals that the local standard deviation of each frequency band is correlated with the local standard deviation of the other frequency bands. The ratio between the standard deviation of adjacent frequency bands is 0.9 and remains constant with respect to time. This ratio defined as the variance coupling parameter is applicable to all of the frequency bands studied and appears to be related to the slope of the data's power spectrum. Similar analyses are performed on two cloud inhomogeneity models, which use fractal-based concepts to introduce inhomogeneity into a uniform cloud field. The bounded cascade model does this by iteratively redistributing LWP at each scale using the value of the local mean. This model is reformulated into a wavelet multiresolution framework, thereby presenting a number of variants of the bounded cascade model. One variant introduced in this paper is the 'variance coupled model,' which redistributes LWP using the local standard deviation and the variance coupling parameter. While the bounded cascade model provides an elegant two- parameter model for generating cloud inhomogeneity, the multiresolution framework provides more flexibility at the expense of model complexity. Comparisons are made with the results from the LWP data analysis to demonstrate both the strengths and weaknesses of these models.

Gollmer, Steven M.↗
NASA NTRS1997

Physics of Rotation Powered Pulsars and Their Nebulae

This letter is my progress report for the Astrophysics Theory grant. The first goal of the research supported by this grant is to produce a time dependent theory of the unsteady relativistic collisionless shock wave terminating the relativistic wind from a pulsar, and compare the predicted surface brightness fluctuations to Hubble Space Telescope observations of the wisps in the Crab Nebula. The second goal is to model the production of electron-positron pairs over the polar caps of rotation powered pulsars, and use the results to predict the heating of the surface due to particle trapping and bombardment of the atmosphere at the base of the polar field lines. We have succeeded in creating a one dimensional hybrid code, in which the electron-positron pairs incident on the shock structure are modeled as a relativistic, adiabatic, ideal MHD fluid, while the heavy ions are treated as particles using a particle-in-cell algorithm. The electromagnetic fields are evaluated from the currents and charge densities in the pairs and the ions, while the particles and the fluid accelerate in response to the computed self-consistent electromagnetic fields. The results are promising, in that the underlying ion cyclotron instability generates finite amplitude, propagating magnetosonic waves in the pairs, whose wavelengths and frequencies, when translated into physical units, are comparable to the observed running waves of brightness observed by HST near the Crab pulsar. The code is undergoing a number of tests, to assure us that this preliminary correspondence is not an artifact. In the coming year, the observational appearance of the models will be computed and compared to the HST observations of the Crab now in hand, and used to predict the HST results which will be obtained the year after next. WE also developed a one dimensional cascade theory for pair creation over pulsars' polar caps. A linear integral equation describing the synchrotron cascade has been derived and solved by iterative techniques, in the case when a high energy electron moving parallel to a star centered dipole magnetic field initiates the cascade through curvature gamma ray emission.

Arons, Jonathan↗
NASA NTRS1996

Spectra of Baroclinic Inertia-Gravity Wave Turbulence

Baroclinic inertia-gravity (IG) waves form a persistent background of thermocline depth and sea surface height oscillations. They also contribute to the kinetic energy of horizontal motions in the subsurface layer. Measured by the ratio of water particle velocity to wave phase speed, the wave nonlinearity may be rather high. Given a continuous supply of energy from external sources, nonlinear wave-wave interactions among IG waves would result in inertial cascades of energy, momentum, and wave action. Based on a recently developed theory of wave turbulence in scale-dependent systems, these cascades are investigated and IG wave spectra are derived for an arbitrary degree of wave nonlinearity. Comparisons with satellite-altimetry-based spectra of surface height variations and with energy spectra of horizontal velocity fluctuations show good agreement. The well-known spectral peak at the inertial frequency is thus explained as a result of the inverse cascade. Finally, we discuss a possibility of inferring the internal Rossby radius of deformation and other dynamical properties of the upper thermocline from the spectra of SSH (sea surface height) variations based on altimeter measurements.

Glazman, Roman E.↗
NASA NTRS1999

Heat Transfer and Flow on the First Stage Blade Tip of a Power Generation Gas Turbine: Experimental Results - Part 1

A combined computational and experimental study has been performed to investigate the detailed distribution of convective heat transfer coefficients on the first stage blade tip surface for a geometry typical of large power generation turbines(>100MW). This paper is concerned with the design and execution of the experimental portion of the study. A stationary blade cascade experiment has been run consisting of three airfoils, the center airfoil having a variable tip gap clearance. The airfoil models the aerodynamic tip section of a high pressure turbine blade with inlet Mach number of 0.30, exit Mach number of 0.75, pressure ratio of 1.45, exit Reynolds number based on axial chord of 2.57 x 10(exp 6), and total turning of about 110 degrees. A hue detection based liquid crystal method is used to obtain the detailed heat transfer coefficient distribution on the blade tip surface for flat, smooth tip surfaces with both sharp and rounded edges. The cascade inlet turbulence intensity level took on values of either 5% or 9%. The cascade also models the casing recess in the shroud surface ahead of the blade. Experimental results are shown for the pressure distribution measurements on the airfoil near the tip gap, on the blade tip surface, and on the opposite shroud surface. Tip surface heat transfer coefficient distributions are shown for sharp-edge and rounded-edge tip geometries at each of the inlet turbulence intensity levels.

Bunker, Ronald S.↗
NASA NTRS1999

Assessment of the Microbial Control Measures for the Temperature and Humidity Control Subsystem Condensing Heat Exchanger of the International Space Station

In August 1997 NASA/ Marshall Space Flight Center (MSFC) began a test with the objective of monitoring the growth of microorganisms on material simulating the surface of the International Space Station (ISS) Temperature and Humidity Control (THC) Condensing Heat Exchanger (CHX). The test addressed the concerns of potential uncontrolled microbial growth on the surface of the THC CHX subsystem. For this study, humidity condensate from a closed manned environment was used as a direct challenge to the surfaces of six cascades in a test set-up. The condensate was collected using a Shuttle-type CHX within the MSFC End-Use Equipment Testing Facility. Panels in four of the six cascades tested were coated with the ISS CHX silver impregnated hydrophilic coating. The remainder two cascade panels were coated with the hydrophilic coating without the antimicrobial component, silver. Results of the fourteen-month study are discussed in this paper. The effects on the microbial population when drying vs. not-drying the simulated THC CHX surface are also discussed.

Roman, Monsi C.↗
NASA NTRS1998

Fluorescence Studies of Lysozyme Nucleation

Fluorescence is one of the most powerful tools available for the study of macromolecules. For example, fluorescence can be used to study self association through methods such as anisotropy (the rotational rate of the molecule in solution), quenching (the accessibility of a bound probe to the bulk solution), and resonance energy transfer (measurement of the distance between two species). Fluorescence can also be used to study the local environment of the probe molecules, and the changes in that environment which accompany crystal nucleation and growth. However fluorescent techniques have been very much underutilized in macromolecular growth studies. One major advantage is that the fluorescent species generally must be at low concentration, typically ca 10-5 to 10-6 M. Thus one can study a very wide range of solution conditions, ranging from very high to very low protein concentration, he latter of which are not readily accessible to scattering techniques. We have prepared a number of fluorescent derivatives of chicken egg white lysozyme (CEWL). Fluorescent probes have been attached to two different sites, ASP 101 and the N-terrninal amine, with a sought for use in different lines of study. Preliminary resonance energy transfer studies have been -carried out using pyrene acetic acid (Ex 340 mn, Em 376 nm) lysozyme as a donor and cascade blue (Ex 377 run, Em 423 nm) labeled lysozyme as an acceptor. The emission of both the pyrene and cascade blue probes was followed as a function of the salt protein concentrations. The data show an increase in cascade blue and a concomitant decrease in the pyrene fluorescence as either the salt or protein concentrations are increased, suggesting that the two species are approaching each other close enough for resonance energy transfer to occur. This data can be analyzed to measure the distance between the probe molecules and, knowing their locations on the protein molecule their distances from and orientations with respect to each other. The results of these and other studies will be discussed.

Pusey, Marc L.↗
NASA NTRS2000

Turbulence Measurements and Computations for the Predication of Broadband Noise in High Bypass Ratio Fans

Work was performed under this grant with a view to providing the experimental and computational results needed to improve the prediction of broadband stator noise in large bypass ratio aircraft engines. The central hypothesis of our study was that a large fraction of this noise was generated by the fan tip leakage vortices. More specifically, that these vortices are a significant component of the fan wake turbulence and they contain turbulent eddies of a type that can produce significant broadband noise. To test this hypothesis we originally proposed experimental work and computations with the following objectives: (1) to build a large scale two-dimensional cascade with a tip gap and a stationary endwall that, as far as possible, simulates the fan tip geometry, (2) to build a moving endwall for use with the large scale cascade, (3) to measure, in detail, the turbulence structure and spectrum generated by the blade wake and tip leakage vortex, for both endwall configurations, (4) to use the CFD to compute the flow and turbulence distributions for both the experimental configurations and the ADP fan, (5) to provide the experimental and CFD results for the cascades and the physical understanding gained from their study as a basis for improving the broadband noise prediction method. In large part these objectives have been achieved. The most important achievements and findings of our experimental and computational efforts are summarized below. The bibliography at the end of this report includes a list of all publications produced to date under this project. Note that this list is necessarily incomplete the task of publication (particularly in journal papers) continues.

Devenport, William J.↗
NASA NTRS2000

Preparation and Characterization of Fluorescent Derivatives of Chicken Egg White Lysozyme

Fluorescence is one of the most versatile and powerful tools for the study of macromolecules. While most proteins are intrinsically fluorescent, working at crystallization concentrations require the use of covalently prepared derivatives added as tracers. This approach requires derivatives that do not markedly affect the crystal packing. We have prepared a number of fluorescent derivatives of chicken egg white lysozyme with probes bound to one of two different sites on the protein molecule. Lucifer yellow, cascade blue, and 5-(2-aminoethyl)aminonapthalene-l-sulfonic acid (EDANS) have been attached to the side chain carboxyl of asp101 using a carbodiimide coupling procedure. asp101 lies within the active site cleft, and it is believed that the probes are at least partially "buried" within that cleft. Lucifer yellow and MANS probes with iodoacetamide reactive groups have been bound to hisl5, located on the "back side" of the molecule relative to the active site. The fluorescently labeled protein is readily purified from the starting material by cation exchange chromatography. All the derivatives fluoresce in both the solution and the crystalline states. Fluorescence characterization has focused on determining the bound probe quantum yields, lifetimes, absorption and emission spectra, and quenching by added solutes in comparison to the free probe. No appreciable changes are found in the lifetimes of any of the probes except for cascade blue, where Tau(sub free) = 3.52 ns vrs Tau(sub bound) = 2.8 ns. Spectral shifts are found in most cases. Particularly strong quenching upon binding is found in the case of the cascade blue derivative, likely due to probe interactions with the active site cleft. While none of the asp101 bound probes are well quenched by commonly employed solutes, such as potassium and sodium iodide, acrylamide, primuline, the chloride salts of manganese, cesium, and cobalt, trifluoroacetamide, trichloroethanol, and thallium iodide, in those cases where quenching is observed the bound probe is less efficiently quenched relative to the free probe. This indicates that the bound probes are less accessible to the bulk solution, an expected finding for attachment within the active site cleft. Attempts have been made to bind other molecules to these sites, with varying success. Interestingly, all three probes contain one or more sulfonate ((Ar-S03)-) groups. We have not been successful in binding analogous probes without sulfate groups such as pyrene, or with derivatized sulfonate groups such as dansyl type probes, analogous to MANS but where the sulfonate group is derivatized, Ar-S02-N2C2H7. None of the probes is rigidly bound to the protein, i.e., they all have a probe motion superimposed on that of the protein.

Sumida, John↗
NASA NTRS2000

Heat Transfer and Flow on the Squealer Tip of a Gas Turbine Blade

Experimental investigations are performed to measure the detailed heat transfer coefficient and static pressure distributions on the squealer tip of a gas turbine blade in a five-bladed stationary linear cascade. The blade is a 2-dimensional model of a modem first stage gas turbine rotor blade with a blade tip profile of a GE-E(sup 3) aircraft gas turbine engine rotor blade. A squealer (recessed) tip with a 3.77% recess is considered here. The data on the squealer tip are also compared with a flat tip case. All measurements are made at three different tip gap clearances of about 1%, 1.5%, and 2.5% of the blade span. Two different turbulence intensities of 6.1% and 9.7% at the cascade inlet are also considered for heat transfer measurements. Static pressure measurements are made in the mid-span and near-tip regions, as well as on the shroud surface opposite to the blade tip surface. The flow condition in the test cascade corresponds to an overall pressure ratio of 1.32 and an exit Reynolds number based on the axial chord of 1.1 x 10(exp 6). A transient liquid crystal technique is used to measure the heat transfer coefficients. Results show that the heat transfer coefficient on the cavity surface and rim increases with an increase in tip clearance. 'Me heat transfer coefficient on the rim is higher than the cavity surface. The cavity surface has a higher heat transfer coefficient near the leading edge region than the trailing edge region. The heat transfer coefficient on the pressure side rim and trailing edge region is higher at a higher turbulence intensity level of 9.7% over 6.1 % case. However, no significant difference in local heat transfer coefficient is observed inside the cavity and the suction side rim for the two turbulence intensities. The squealer tip blade provides a lower overall heat transfer coefficient when compared to the flat tip blade.

Azad, Gm S.↗
NASA NTRS2000

Heat Transfer and Pressure Distributions on a Gas Turbine Blade Tip

Heat transfer coefficient and static pressure distributions are experimentally investigated on a gas turbine blade tip in a five-bladed stationary linear cascade. The blade is a 2-dimensional model of a first stage gas turbine rotor blade with a blade tip profile of a GE-E(sup 3) aircraft gas turbine engine rotor blade. The flow condition in the test cascade corresponds to an overall pressure ratio of 1.32 and exit Reynolds number based on axial chord of 1.1 x 10(exp 6). The middle 3-blade has a variable tip gap clearance. All measurements are made at three different tip gap clearances of about 1%, 1.5%, and 2.5% of the blade span. Heat transfer measurements are also made at two different turbulence intensity levels of 6.1 % and 9.7% at the cascade inlet. Static pressure measurements are made in the mid-span and the near-tip regions as well as on the shroud surface, opposite the blade tip surface. Detailed heat transfer coefficient distributions on the plane tip surface are measured using a transient liquid crystal technique. Results show various regions of high and low heat transfer coefficient on the tip surface. Tip clearance has a significant influence on local tip beat transfer coefficient distribution. Heat transfer coefficient also increases about 15-20% along the leakage flow path at higher turbulence intensity level of 9.7% over 6.1 %.

Azad, Gm S.↗
NASA NTRS2000

Static Performance of Six Innovative Thrust Reverser Concepts for Subsonic Transport Applications: Summary of the NASA Langley Innovative Thrust Reverser Test Program

The NASA Langley Configuration Aerodynamics Branch has conducted an experimental investigation to study the static performance of innovative thrust reverser concepts applicable to high-bypass-ratio turbofan engines. Testing was conducted on a conventional separate-flow exhaust system configuration, a conventional cascade thrust reverser configuration, and six innovative thrust reverser configurations. The innovative thrust reverser configurations consisted of a cascade thrust reverser with porous fan-duct blocker, a blockerless thrust reverser, two core-mounted target thrust reversers, a multi-door crocodile thrust reverser, and a wing-mounted thrust reverser. Each of the innovative thrust reverser concepts offer potential weight savings and/or design simplifications over a conventional cascade thrust reverser design. Testing was conducted in the Jet-Exit Test Facility at NASA Langley Research Center using a 7.9%-scale exhaust system model with a fan-to-core bypass ratio of approximately 9.0. All tests were conducted with no external flow and cold, high-pressure air was used to simulate core and fan exhaust flows. Results show that the innovative thrust reverser concepts achieved thrust reverser performance levels which, when taking into account the potential for system simplification and reduced weight, may make them competitive with, or potentially more cost effective than current state-of-the-art thrust reverser systems.

Asbury, Scott C.↗
NASA NTRS2001

Broadband Noise of Fans - With Unsteady Coupling Theory to Account for Rotor and Stator Reflection/Transmission Effects

This report examines the effects on broadband noise generation of unsteady coupling between a rotor and stator in the fan stage of a turbofan engine. Whereas previous acoustic analyses treated the blade rows as isolated cascades, the present work accounts for reflection and transmission effects at both blade rows by tracking the mode and frequency scattering of pressure and vortical waves. The fan stage is modeled in rectilinear geometry to take advantage of a previously existing unsteady cascade theory for 3D perturbation waves and thereby use a realistic 3D turbulence spectrum. In the analysis, it was found that the set of participating modes divides itself naturally into "independent mode subsets" that couple only among themselves and not to the other such subsets. This principle is the basis for the analysis and considerably reduces computational effort. It also provides a simple, accurate scheme for modal averaging for further efficiency. Computed results for a coupled fan stage are compared with calculations for isolated blade rows. It is found that coupling increases downstream noise by 2 to 4 dB. Upstream noise is lower for isolated cascades and is further reduced by including coupling effects. In comparison with test data, the increase in the upstream/downstream differential indicates that broadband noise from turbulent inflow at the stator dominates downstream noise but is not a significant contributor to upstream noise.

Hanson, Donald B.↗
NASA NTRS2001

Use of Pressure Sensitive Paint for Diagnostics in Turbomachinery Flows With Shocks

The technology of pressure sensitive paint (PSP) is well established in external aerodynamics. In internal flows in narrow channels and in turbomachinery cascades, however, there are still unresolved problems. In particular, the internal flows with complex shock structures inside highly curved channels present a challenge. It is not always easy and straightforward to distinguish between true signals and "ghost" images due to multiple internal reflections in narrow channels. To address some of the problems, investigations were first carried out in a narrow supersonic channel of Mach number 2.5. A single wedge or a combination of two wedges were used to generate a complex shock wave structure in the flow. The experience gained in a small supersonic channel was used for surface pressure measurements on the stator vane of a supersonic throughflow fan. The experimental results for several fan operating conditions are shown in a concise form, including performance map points, midspan static tap pressure distributions, and vane suction side pressure fields. Finally, the PSP technique was used in the NASA transonic flutter cascade to compliment flow visualization data and to acquire backwall pressure fields to assess the cascade flow periodicity. A summary of shortcomings of the pressure sensitive paint technology for internal flow application and lessons learned are presented in the conclusion of the paper.

Lepicovsky, Jan↗
NASA NTRS2001

Stochastic Particle Acceleration in Impulsive Solar Flares

The acceleration of a huge number of electrons and ions to relativistic energies over timescales ranging from several seconds to several tens of seconds is the fundamental problem in high-energy solar physics. The cascading turbulence model we have developed has been shown previously (e.g., Miller 2000; Miller & Roberts 1995; Miner, LaRosa, & Moore 1996) to account for all the bulk features (such as acceleration timescales, fluxes, total number of energetic particles, and maximum energies) of electron and proton acceleration in impulsive solar flares. While the simulation of this acceleration process is involved, the essential idea of the model is quite simple, and consists of just a few parts: 1. During the primary flare energy release phase, we assume that low-amplitude MHD Alfven and fast mode waves are excited at long wavelengths, say comparable to the size of the event (although the results are actually insensitive to this initial wavelength). While an assumption, this appears reasonable in light of the likely highly turbulent nature of the flare. 2. These waves then cascade in a Kolmogorov-like fashion to smaller wavelengths (e.g., Verma et al. 1996), forming a power-law spectral density in wavenumber space through the inertial range. 3. When the mean wavenumber of the fast mode waves has increased sufficiently, the transit-time acceleration rate (Miller 1997) for superAlfvenic electrons can overcome Coulomb energy losses, and these electrons are accelerated out of the thermal distribution and to relativistic energies (Miller et al. 1996). As the Alfven waves cascade to higher wavenumbers, they can cyclotron resonate with progressively lower energy protons. Eventually, they will resonate with protons in the tail of the thermal distribution, which will then be accelerated to relativistic energies as well (Miller & Roberts 1995). Hence, both ions and electrons are stochastically accelerated, albeit by different mechanisms and different waves. 4. When the protons become superAlfvenic (above about 1 MeV/nucleon), they too can suffer transit-time acceleration by the fast mode waves and will receive an extra acceleration "kick." The basic overall objective of this 1 year effort was to construct a spatially-dependent version of this acceleration model and this has been realized.

Miller, James A.↗
NASA NTRS2003

Unified Models of Turbulence and Nonlinear Wave Evolution in the Extended Solar Corona and Solar Wind

The PI (Cranmer) and Co-I (A. van Ballegooijen) made significant progress toward the goal of building a "unified model" of the dominant physical processes responsible for the acceleration of the solar wind. The approach outlined in the original proposal comprised two complementary pieces: (1) to further investigate individual physical processes under realistic coronal and solar wind conditions, and (2) to extract the dominant physical effects from simulations and apply them to a one-dimensional and time-independent model of plasma heating and acceleration. The accomplishments in the report period are thus divided into these two categories: 1a. Focused Study of Kinetic MHD Turbulence. We have developed a model of magnetohydrodynamic (MHD) turbulence in the extended solar corona that contains the effects of collisionless dissipation and anisotropic particle heating. A turbulent cascade is one possible way of generating small-scale fluctuations (easy to dissipate/heat) from a pre-existing population of low-frequency Alfven waves (difficult to dissipate/heat). We modeled the cascade as a combination of advection and diffusion in wavenumber space. The dominant spectral transfer occurs in the direction perpendicular to the background magnetic field. As expected from earlier models, this leads to a highly anisotropic fluctuation spectrum with a rapidly decaying tail in the parallel wavenumber direction. The wave power that decays to high enough frequencies to become ion cyclotron resonant depends on the relative strengths of advection and diffusion in the cascade. For the most realistic values of these parameters, though, there is insufficient power to heat protons and heavy ions. The dominant oblique waves undergo Landau damping, which implies strong parallel electron heating. We thus investigated the nonlinear evolution of the electron velocity distributions (VDFs) into parallel beams and discrete phase-space holes (similar to those seen in the terrestrial magnetosphere) which are an alternate means of heating protons via stochastic interactions similar to particle-particle collisions. 1b. Focused Study of the Multi-Mode Detailed Balance Formalism. The PI began to explore the feasibility of using the "weak turbulence," or detailed-balance theory of Tsytovich, Melrose, and others to encompass the relevant physics of the solar wind. This study did not go far, however, because if the "strong" MHD turbulence discussed above is a dominant player in the wind's acceleration region, this formalism is inherently not applicable to the corona. We will continue to study the various published approaches to the weak turbulence formalism, especially with an eye on ways to parameterize nonlinear wave reflection rates. 2. Building the Unified Model Code Architecture. We have begun developing the computational model of a time-steady open flux tube in the extended corona. The model will be "unified" in the sense that it will include (simultaneously for the first time) as many of the various proposed physical processes as possible, all on equal footing. To retain this generality, we have formulated the problem in two interconnected parts: a completely kinetic model for the particles, using the Monte Carlo approach, and a finite-difference approach for the self-consistent fluctuation spectra. The two codes are run sequentially and iteratively until complete consistency is achieved. The current version of the Monte Carlo code incorporates gravity, the zero-current electric field, magnetic mirroring, and collisions. The fluctuation code incorporates WKJ3 wave action conservation and the cascade/dissipation processes discussed above. The codes are being run for various test problems with known solutions. Planned additions to the codes include prescriptions for nonlinear wave steepening, kinetic velocity-space diffusion, and multi-mode coupling (including reflection and refraction).

Cranmer, Steven R.↗