The Structure of Stratospheric Irregularities According to Radio-Occultation Data Obtained using Satellite-to-Satellite Paths

We analyze the possibility of monitoring density or temperature fluctuations in the stratosphere based on data of amplitude radio-occultation measurements at centimeter waves using satellite-to-satellite paths. Comparison of the experimental spectra of amplitude fluctuations with the theoretical spectra calculated for a model containing both strongly anisotropic irregularities and an isotropic Kolmogorov turbulence shows that the amplitude fluctuations of radio waves in the stratosphere are mainly contributed by anisotropic irregularities which correspond to the model of saturated internal gravity waves. The efficiency of the radio occultation technique for the global remote monitoring of internal waves in the stratosphere is demonstrated.     

Background fluctuations in the GPS-microlab-1 ionospheric radio sounding experiment

We analyze the spectra of the phase and amplitude fluctuations of radio signals recorded in the course of four ionospheric radio-sounding sessions at altitudes from 70 to 120 km. Our study is aimed at determining the sources of these fluctuations. Comparing the statistical properties of fluctuations measured at two wavelengths with theoretical calculations, we conclude that only the low-frequency part of background fluctuations is of ionospheric origin, while the high-frequency fluctuations are caused by noise of the measuring system. The amplitude fluctuations are more informative in the high-frequency region, since they are mainly due to ionospheric irregularities. We discuss the possibility of separation of the components of amplitude fluctuations caused by ionospheric irregularities and the irregularities of the neutral atmosphere in the case of sounding at the altitudes at which those components have comparable values. It is shown that this problem cannot be solved by dispersion and extrapolation methods, which are used for separation of the regular ionospheric and atmospheric components of the amplitude and phase variations of radio signals. A. N. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Moscow, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 6, pp. 511–523, June 1999.     

Amplitude and Phase Fluctuations of Decimeter Radio Waves Raying the Atmosphere via Satellite-to-Satellite Paths

We present the results of experimental studies of the atmospheric phase and amplitude fluctuations of decimeter radio waves in radio occultation measurements using paths connecting the MICROLAB satellite and the satellites of the GPS navigation system. The dependences of the amplitude- and phase-fluctuation variance on the minimum altitude of the ray trajectory and the frequency spectra of the fluctuations are presented. The experimental data are compared with the theory of radio-wave propagation in random media. We determine the spectral index of irregularities of the atmospheric refractive index, the external scale of the irregularities, and the variance of the refractive-index fluctuations. It is shown that the radio occultation technique allows one to monitor small-scale irregularities of the atmosphere.     

Application of the method of nonstationary waveguide equations to simulating pulsed processes in irregular transmission lines

The potentialities of the model of nonstationary waveguide equations for describing pulsed processes in irregular transmission lines are studied using planar lines as an example. The problem of high-accuracy controllable-error numerical simulation is discussed. Typical examples of simulating ultra-wide-band electromagnetic pulses with an initial TEM structure in terms of time-domain representation are presented with emphasis on the interaction of the pulses with irregularities, including their transformation into longitudinal waves. Both lumped and distributed irregularities are addressed: deep corrugations that cover 90% of the transmission line’s aperture (distributed irregularities) and these corrugations in combination with sharp kinks at the boundary surfaces and permittivity steps at the boundaries of the dielectric filling (lumped irregularities). It is shown that a relative rms error involved in the calculated field intensity of no higher than 10⁻⁴ is easy to achieve.     

Attenuation of a Stoneley wave and higher Lamb modes due to the scattering by two-dimensional irregularities of the walls of a fluid-filled borehole

Attenuation of Stoneley waves and higher Lamb modes propagating along an irregular surface of a fluid-filled borehole is investigated. This problem generalizes the problem on the attenuation of Rayleigh waves by an irregular surface of an empty borehole [10]. The technique used to evaluate the attenuation coefficient is based on the perturbation method (surface irregularity heights are considered to be small in comparison with the wavelength) and the mean field method. As a result, an expression is obtained for the partial coefficients of the eigenmode attenuation due to the scattering of eigenmodes by the irregularities of the borehole walls into the same or other eigenmodes, as well as into the bulk longitudinal and transverse waves. The frequency-dependent behavior of the partial attenuation coefficients of both Stoneley waves and higher modes is analyzed against the ratio between the irregularity correlation length and the borehole radius for different correlation functions of irregularities.     

Berkhoff approximation in a problem on surface gravity wave propagation in a basin with bottom irregularities

The problem of the propagation of small-amplitude surface gravity waves in a basin of constant mean depth with one- and two-dimensional bottom roughness is solved in the framework of the Berkhoff model by a mean-field method. In both cases the solutions obtained are compared with the solutions of sets of exact linearized equations of the hydrodynamics of an incompressible fluid. The comparison of the exact and approximate mean-field attenuation coefficients has shown that the Berkhoff approximation is appropriate for the solution of this problem in the case of shallow water for an arbitrary correlation length of bottom irregularities and in the case of arbitrary depth and large-scale irregularities. An explanation is given for the limits of applicability of the Berkhoff approximation which are connected with the weak variability of the vertical structure of the wave field in shallow water and in a basin with large-scale depth fluctuations. The mean-field attenuation coefficients reach their maximum values in the region k_oh_o≥1 (where k_o is the wavenumber of the surface gravity wave in a basin of constant depth h_o). The location of these maxima is practically independent of the correlation length of the bottom irregularities. For the case of one-dimensional irregularities the effect of bottom roughness on the surface gravity wave velocity is investigated. It is shown that the surface wave in a basin with an uneven bottom may propagate more slowly, as well as faster than the wave in a basin with an even bottom, depending on the relations between the wavelength, depth and correlation length of the bottom imperfections.     

Angular dependence of proton inclusive spectra from dp → pX reaction at 3.34 GeV/c

Inclusive differential cross sections for the dp → pX reaction at 3.34 GeV/c are presented for different proton production angles in the deuteron frame. At large angles some irregularities have been observed in the spectra. The obtained angular dependence of the inclusive differential spectra for the backward hemisphere allows a detailed comparison with models describing dp interactions. This comparison shows the importance to consider the contributions from rescattering processes at production angles around 90°. Conclusion is made about the necessity to involve additional mechanisms into existing models in order to describe the angular dependence of the inclusive proton cross sections.     

Turbulence spectrum of the upper ionosphere

The problem of defining the spectral form of ionospheric irregularities with dimensions from hundreds to thousands of meters is considered. A generalized model is proposed for the ionospheric turbulence spectrum, taking into account both the anisotropic properties of the large-scale fraction of irregularities and the dependence of the anisotropy (elongation) of small-scale irregularities of the upper ionosphere along the Earth magnetic field direction on the transverse scale of those irregularities. Relations have been derived to determine the basic parameters of the irregularity spectrum of the uppers ionosphere (anisotropy indices for large-scale and small-scale fractions) and the depth of a thin ionospheric layer through measurement of the spectral characteristics of amplitude and phase fluctuations of orbital satellite signals. Using this model of the plasma irregularity spectrum, we can explain consistently many well-known experimental data on spectral characteristics of the phase and amplitude fluctuations of orbital satellite signals both in the high-latitude and midlatitude ionosphere. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 4, pp. 446–456, April, 1997.     

Nonlinear structuring of the ionosphere modified by powerful radio waves at low latitudes

The problem of the nonlinear structuring of the modified ionosphere due to the self-focusing of the pump wave on the bunches of striations is investigated. Two main conditions of self-focusing are formulated: (1) propagation of the pump wave quite along the magnetic field for effective excitation of striations, and (2) trapping of the pump wave by large-scale irregularities. It is shown that both conditions can be easily satisfied for small inclination angles α of the magnetic field to the vertical. A detailed study of the low latitude case was performed using model calculations of the pump wave propagation. It is shown that at low latitudes self-focusing conditions also can be satisfied but mostly for the special form of the large-scale irregularities and mostly in the southern part of the pump wave beam. These results may reconcile apparent differences between radiowave and rocket probing of the irregularities.     

Solitary wave dynamics in shallow water over periodic topography

The problem of long-wave scattering by piecewise-constant periodic topography is studied both for a linear solitary-like wave pulse, and for a weakly nonlinear solitary wave [Korteweg-de Vries (KdV) soliton]. If the characteristic length of the topographic irregularities is larger than the pulse length, the solution of the scattering problem is obtained analytically for a leading wave in the framework of linear shallow-water theory. The wave decrement in the case of the small height of the topographic irregularities is proportional to delta2, where delta is the relative height of the topographic obstacles. An analytical approximate solution is also obtained for the weakly nonlinear problem when the length of the irregularities is larger than the characteristic nonlinear length scale. In this case, the Korteweg-de Vries equation is solved for each piece of constant depth by using the inverse scattering technique; the solutions are matched at each step by using linear shallow-water theory. The weakly nonlinear solitary wave decays more significantly than the linear solitary pulse. Solitary wave dynamics above a random seabed is also discussed, and the results obtained for random topography (including experimental data) are in reasonable agreement with the calculations for piecewise topography.     

Theory of scanning capacitance microscopy

The theory of scanning capacitance microscopy (SCM), used in the examination of a two-dimensional distribution of irregularities in films arranged over metallic substrates, as well as of reliefs of conductive surfaces, is discussed. A realistic model of SCM, which is solvable analytically, is proposed. An explicit solution of the inverse problem of irregularities relief reconstruction (IRR) in SCM is obtained. The possible effects resulting from exciting of free oscillations in the “film-stylus” system of a sonde microscope are analyzed in detail.     

Excitation of an Additional Region of Short-Wavelength Plasma Oscillations in Ionospheric Heating Experiments

We discuss transfer of plasma waves, excited by a powerful radio wave due to its scattering on artificial ionospheric irregularities, into an additional region of very short plasma oscillations polarized almost perpendicular to the magnetic field. Such a region can exist in the magnetized ionospheric plasma due to the strong spatial dispersion. We take into account the plasma-wave diffusion over the spectrum caused by multiple scattering on irregularities, as well as the nonlinear process of plasma-wave interaction due to induced scattering by ions. The latter process leads to the transfer of primary plasma waves into the additional region. The induced scattering is considered in the differential approximation valid for sufficiently smooth plasma-wave spectra. The numerical calculations are performed for a Maxwellian plasma in which suprathermal electrons are absent. It is shown that in this case, the additional region of plasma waves is excited if the pump frequency is close to but slightly less than the fourth electron gyroharmonic, so that the absorption of primarily excited plasma waves becomes sufficiently strong. Application of our calculations to the results of ionospheric experiments is discussed.     

Ionospheric plasma by VHF waves

The amplitude scintillations of very high frequency electromagnetic wave transmitted from geo-stationary satellite at 244.168 MHz have been recorded at Varanasi (geom. lat. 14′ 55′N) during 1991 to 1999. The data are analyzed to determine the statistical features of overhead ionospheric plasma irregularities which are mostly of small duration <30 minutes and are predominant during pre-midnight period. The increase of solar activity generally increases the depth of scintillation. The auto-correlation functions and power spectra of scintillations predict that the scale length of these irregularities varies from 200–500 m having velocity of movement between 75 m/sec to 200 m/sec. These results agree well with the results obtained by other workers.     

Strong scintillation spectra behind a phase screen containing large-scale anisotropic irregularities

Using the approximation of an anisotropic statistically-homogeneous phase screen, we consider spectra of strong scintillations. Numerical calculations are made for the model of large-scale anisotropic inhomogeneities typical of the Earth’s stratosphere. The spectrum transformation is studied for the transition from weak scintillations to the asymptotic regime of strong scintillations. We show that with increasing level of the scintillations, their spectra rapidly broaden to the region of large wave numbers which exceed both the inverse internal scale of the irregularities and the inverse radius of the Fresnel zone by orders of magnitude. Notable deviations of the two-dimensional spectra from the predictions based on perturbation theory are shown to occur for scintillation variance exceeding 0.1. The obtained two-dimensional spectra of scintillations give a complete picture of the behavior of one-dimensional spectra which can be retrieved from satellite observations made for different angles between the orbit plane and the direction to the source. Vertical and horizontal one-dimensional spectra are studied in detail. Approximate algebraic formulas are derived and their validity is proved by applying them to the calculation of spectra of strong scintillations for a wide (several decades) range of the wave number values. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 9, pp. 747–765, September 2007.     

Path integrals for wave intensity fluctuations in random media

Approximate expressions for the fourth order moment of a wave propagating in a random medium are derived by using the path integral formulation. These solutions allow the spectrum of intensity fluctuations of a multiply scattered wave to be found, and they are valid at all distances in the medium. The results obtained by path integral methods turn out to be the same as those obtained previously by solving the parabolic partial differential equation for the fourth moment. The spatial frequency spectra of intensity fluctuations are evaluated for a medium in which the irregularities have a single scale and also for one in which there is a range of scale sizes.     

Calculation of low-frequency sound fields in irregular waveguides with strong backscattering

An approach is developed for calculating the sound fields in a non-stratified sea medium with irregularities that are not weak. The method of cross sections for horizontal parts of acoustic modes is used to obtain first-order causal equations that are equivalent to the boundary-value problem. A matrix equation describing the backscattered field of modes is analyzed, and the conditions that determine the weakness of the irregularities of the medium and the validity of the known approximate methods of sound field calculations are considered. The approximation of unidirectional propagation is represented in the form of quadratures. The example of a 2D shallow-water waveguide with a strongly irregular profile of a perfectly rigid bottom is considered to illustrate the advantages of the proposed approach in comparison with the approximate methods for specific low frequencies. The qualitative and quantitative differences that arise because of taking into account the backscattering between the curves of propagation losses corresponding to the exact solution and the conventional approximate methods are discussed.     

Double-deck structure of the boundary layer in the problem of flow in an axially symmetric pipe with small irregularities on the wall for large Reynolds numbers

The problem of flow of a viscous incompressible fluid in an axially symmetric pipe with small irregularities on the wall is considered. An asymptotic solution of the problem with the double-deck structure of the boundary layer and the unperturbed flow in the environment (the “core flow”) is obtained. The results of flow numerical simulation in the thin and “thick” boundary layers are given.     

Parameterization of the magnetite coating surfaces on low-carbon steel with the use of atomic force microscopy data

The atomic force microscopy (AFM) technique is used to obtain information on the dynamic behavior of the magnetite coating (MC) formed on a steel 3 (St3) sample by chemical oxidation in a solution of ammonium nitrate. Digitized AFM data are the sets of profiles of chaotic roughness obtained via a sensing probe scanning over the surface fragment under study. The flicker noise spectroscopy (FNS) technique is used to analyze AFM images and to select parameters adapted to MC state characterization at the initial stages of formation. The FNS parameters introduced to characterize coating surfaces are calculated from spatial power spectra and transient structure functions. These parameters are considered to be the correlation lengths for different-type irregularities (jumps and spikes). Additionally, dimensionless parameters are introduced to characterize the loss of correlation in a series of irregularities when spatial intervals are substantially less than the correlation lengths. The performed FNS parameterization enabled us to obtain information on the state of the initial surface of St3 samples and to reveal the structural features intrinsic to the surface of MCs formed after different periods of oxidation. This information determines correlations between the elements of the MC structure and characterizes the properties of its microirregularities arising at different stages of coating formation.     

Effect of random density irregularities on nonlinear evolution of Langmuir waves in interplanetary medium

The evolution of nonlinear Langmuir waves in the interplanetary medium is investigated by appropriately accounting for the random density irregularities of the medium. A pair of modified Zakharov equations, which describe these waves, is solved numerically as an initial value problem for large scale (≫ 10² km) initial pertubations. For an ion acoustic-Langmuir solitary wave, the random irregularities damp the Langmuir wave by way of scattering and let the ion density perturbation radiate away in a few days. However an initial solitary or shock-like Langmuir wave excites the ion density perturbations within a fraction of a second, and then itself gets damped. These effects will strongly decelerate the collapse of large scale Langmuir waves. The possibility of detecting these processes, by means of interplanetary scintillation, is discussed. The authors felicitate Prof. D S Kothari on his eightieth birthday and dedicate this paper to him on this occasion.     

Boundary-condition transformation in problems of electromagnetic-wave scattering by an uneven impedance surface

A rigorous method is developed for transforming a boundary-value problem of electrodynamics in a domain with an uneven boundary to an equivalent problem in a domain with a boundary of a new form. The resulting problem is reduced to an integral boundary equation. This equation is solved by expansion into a series in powers of a small parameter, which is determined by the height of the irregularities in the case of a rough boundary. Impedance corrections for roughness-both determinate and randomare found for an underlying surface of arbitrary form in an inhomogeneous medium.Kharkov State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 3-–, pp. 240–257, March–April, 1993.