On the theoretical computation of the field of low frequency electromagnetic waves over the earth's surface
Explore the source record for details and available documents.
SEARCH · Search NASA
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Explore the source record for details and available documents.
In this paper, we apply two theoretical turbulence models, DIA and the recent GISS model, to study properties of a turbulent channel flow. Both models provide a turbulent kinetic energy spectral function E(k) as the solution of a non-linear equation; the two models employ the same source function but different closures. The source function is characterized by a rate n sub s (k) which is derived from the complex eigenvalues of the Orr--Sommerfeld (OS) equation in which the basic flow is taken to be of a Poiseuille type. The O--S equation is solved for a variety of Reynolds numbers corresponding to available experimental data. A physical argument is presented whereby the central line velocity characterizing the basic flow, U0 sup L, is not to be identified with the U0 appearing in the experimental Reynolds number. The theoretical results are compared with two types of experimental data: (1) turbulence bulk properties, and (2) properties that depend stongly on the structure of the turbulence spectrun at low wave numbers. The only existing analytical expression for Pi (k) cannot be used in the present case because it applies to the case of a flat plate, not a finite channel.
Models to estimate the reflection coefficient of a statistically rough surface, for example the works of Beckmann, Smith, and Vesecky are discussed. Bistatic radar experiments carried out during the Apollo 16 mission provide a data set with which to compare theoretical models and experimental data. These bistatic S-band radar experiments provide experimental estimates of the Moon's bistatic, forward scatter, reflection coefficient for grazing angles of 2.5 to 78 deg. Theoretical expressions for the reflection coefficient are developed for comparison with these experimental data. At grazing angles below 10 deg the models of Smith and Vesecky compare favorably with the data. Beckmann's model falls significantly more rapidly with decreasing grazing angle than does the data.
For an incident plane wave, the field inside a thin scatterer (disk and needle) is estimated by the generalized Rayleigh-Gans (GRG) approximation. This leads to a scattering amplitude tensor equal to that obtained via the Rayleigh approximation (dipole term) with a modifying function. For a finite-length cylinder the inner field is estimated by the corresponding field for the same cylinder of infinite lenght. The effects of different approaches in estimating the field inside the scatterer on the backscattering cross section are illustrated numerically for a circular disk, a needle, and a finite-length cylinder as a function of the wave number and the incidence angle. Finally, the modeling predictions are compared with measurements.
The present investigation of coherent field propagation notes, upon solving the Foldy-Twersky integral equation for a half-space of small spherical scatterers illuminated by a plane wave at oblique incidence, that the coherent field for a horizontally-polarized incident wave exhibits reflectivity and transmissivity consistent with the Fresnel formula for an equivalent continuous effective medium. In the case of a vertically polarized incident wave, both the vertical and longitudinal waves obtained for the coherent field have reflectivities and transmissivities that do not agree with the Fresnel formula.
Algebraic expressions in terms of elementary mathematical functions are derived for power absorption and dissipation by eddy currents and magnetic hysteresis in ferrite spheres. Skin depth is determined by using a variable inner radius in descriptive integral equations. Numerical results are presented for sphere diameters less than one wavelength. A generalized power absorption parameter for both eddy currents and hysteresis is expressed in terms of the independent parameters involving wave frequency, sphere radius, resistivity, and complex permeability. In general, the hysteresis phenomenon has a greater sensitivity to these independent parameters than do eddy currents over the ranges of independent parameters studied herein. Working curves are presented for obtaining power losses from input to the independent parameters.
A vegetation medium is modeled as a half-space of randomly distributed and oriented leaves of arbitrary shape. In accordance with the first-order radiative transfer theory, the backscattering coefficient for such a half-space is expressed in terms of the scattering amplitudes. For disc- or needle-shaped leaves, the generalized Rayleigh-Gans approximation is used to calculate the scattering amplitudes. This approach is valid for leaf dimensions up to the size of the incident wavelength. To examine the leaf-shape effect, elliptic discs are used to model deciduous leaves, and needles are used to model coniferous leaves. The differences between the scattering characteristics of leaves of different shapes are illustrated numerically for various orientations, frequencies, and incidence angles. It is found that the scattering characteristics of elliptic disc-shaped leaves are sensitive to the three angles of orientation and disc ellipticity. In general, both like and cross polarizations may be needed to differentiate the difference in scattering due to the shapes of the leaves.
In this paper, we apply two theoretical turbulence models, DIA and the recent GISS model, to study properties of a turbulent channel flow. Both models provide a turbulent kinetic energy spectral function E(k) as the solution of a non-linear equation; the two models employ the same source function but different closures. The source function is characterized by a rate n sub s (k) which is derived from the complex eigenvalues of the Orr-Sommerfeld (OS) equation in which the basic flow is taken to be of a Poiseuille type. The O-S equation is solved for a variety of Reynolds numbers corresponding to available experimental data. A physical argument is presented whereby the central line velocity characterizing the basic flow, U0 sup L, is not to be identified with the U0 appearing in the experimental Reynolds number. The theoretical results are compared with two types of experimental data: (1) turbulence bulk properties, and (2) properties that depend strongly on the structure of the turbulence spectrum at low wave numbers. The only existing analytical expression for Pi (k) cannot be used in the present case because it applies to the case of a flat plate, not a finite channel.
A set of parallel plasma layers is generated by two intersecting microwave pulses in a chamber containing dry air at a pressure comparable to the upper atmosphere. The dependencies of breakdown conditions on the pressure and pulse length are examined. The results are shown to be consistent with the appearance of tail erosion of the microwave pulse caused by air breakdown. A Bragg scattering experiment, using the plasma layers as a Bragg reflector, is then performed. Both time domain and frequency domain measurements of wave scattering are conducted. The experimental results are found to agree very well with the theory.
A finite-element Galerkin formulation was used to study the effect of material surface deposits on the reflective characteristics of straight uniform ducts with PEC (perfectly electric conducting) walls. Over a wide frequency range, the effect of both single and multiple surface deposits on the duct reflection coefficient were examined. The power reflection coefficient was found to be significantly increased by the addition of deposits on the wall.
A forested canopy is modeled by a collection of randomly oriented finite-length cylinders shaded by randomly oriented and distributed disk- or needle-shaped leaves. For a plane wave exciting the forested canopy, the extinction coefficient is formulated in terms of the extinction cross sections (ECSs) in the local frame of each forest component and the Eulerian angles of orientation (used to describe the orientation of each component). The ECSs in the local frame for the finite-length cylinders used to model the branches are obtained by using the forward-scattering theorem. ECSs in the local frame for the disk- and needle-shaped leaves are obtained by the summation of the absorption and scattering cross-sections. The behavior of the extinction coefficients with the incidence angle is investigated numerically for both deciduous and coniferous forest. The dependencies of the extinction coefficients on the orientation of the leaves are illustrated numerically.
The effective-medium approximation is applied to investigate scattering from a half-space of randomly and densely distributed discrete scatterers. Starting from vector wave equations, an approximation, called effective-medium Born approximation, a particular way, treating Green's functions, and special coordinates, of which the origin is set at the field point, are used to calculate the bistatic- and back-scatterings. An analytic solution of backscattering with closed form is obtained and it shows a depolarization effect. The theoretical results are in good agreement with the experimental measurements in the cases of snow, multi- and first-year sea-ice. The root product ratio of polarization to depolarization in backscattering is equal to 8; this result constitutes a law about polarized scattering phenomena in the nature.
The electron cyclotron maser instability (CMI) driven by momentum space anisotropy (df/dp (sub perpendicular) greater than 0) has been invoked to explain many aspects, such as the modes of propagation, harmonic emissions, and the source characteristics of the auroral kilometric radiation (AKR). Recent satellite observations of AKR sources indicate that the source regions are often imbedded within the auroral acceleration region characterized by the presence of a field-aligned potential drop. In this paper we investigate the excitation of the fundamental extraordinary mode radiation due to the accelerated electrons. The momentum space distribution of these energetic electrons is modeled by a realistic upward loss cone as modified by the presence of a parallel potential drop below the observation point. On the basis of linear growth rate calculations we present the emission characteristics, such as the frequency spectrum and the emission angular distribution as functions of the plasma parameters. We will discuss the implication of our results on the generation of the AKR from the edges of the auroral density cavities.
Many new Earth remote-sensing instruments are embracing both the advantages and added complexity that result from interferometric or fully polarimetric operation. To increase instrument understanding and functionality a model of the signals these instruments measure is presented. A stochastic model is used as it recognizes the non-deterministic nature of any real-world measurements while also providing a tractable mathematical framework. A stationary, Gaussian-distributed model structure is proposed. Temporal and spectral correlation measures provide a statistical description of the physical properties of coherence and polarization-state. From this relationship the model is mathematically defined. The model is shown to be unique for any set of physical parameters. A method of realizing the model (necessary for applications such as synthetic calibration-signal generation) is given and computer simulation results are presented. The signals are constructed using the output of a multi-input multi-output linear filter system, driven with white noise.
We review observations of nonlinear plasma waves detected by interplanetary spacecraft. For this paper we will focus primarily on the phase-steepened properties of such waves. Plasma waves at comet Giacobini-Zinner measured by the International Cometary Explorer (ICE), at comets Halley and Grigg-Skjellerup measured by Giotto, and interplanetary Alfven waves measured by Ulysses, will be discussed and intercompared.
Explore the source record for details and available documents.
Explore the source record for details and available documents.
Explore the source record for details and available documents.