Wave propagation and earth satellite radio emission studies

Radio propagation studies of the ionosphere using satellite radio beacons are described. The ionosphere is known as a dispersive, inhomogeneous, irregular and sometimes even nonlinear medium. After traversing through the ionosphere the radio signal bears signatures of these characteristics. A study of these signatures will be helpful in two areas: (1) It will assist in learning the behavior of the medium, in this case the ionosphere. (2) It will provide information of the kind of signal characteristics and statistics to be expected for communication and navigational satellite systems that use the similar geometry

Modelling Of Downhole Seismic Sources I: Literature Review, Review Of Fundamentals, Impulsive Point Source In A Borehole

This paper represents the first of a two paper sequence comprising a multi-faceted introduction to the numerical and analytical modelling of seismic sources in a borehole. Part one will present a literature review and a review of the fundamental mathematical descriptions of wave propagation outside a borehole. By listing the mathematical descriptions here we can show the equivalence and interrelationships of many treatments presented in the literature. Part one will conclude with an outline of the familiar discrete wavenumber technique as applied to modelling radiation outside a borehole from a point source inside a borehole. Part two will attempt to isolate the effects of the fluid-filled borehole on the radiation of a borehole source by comparing radiation patterns for three cases: a point source in an infinite medium, a stress applied to the wall of an empty borehole (Heelan's (1953) result) and a point source in a fluid-filled borehole (Lee and Balch, 1982). Heelan's results will also be analyzed and defended against criticism of them brought by Jordan (1962) and Abo-Zena (1978). The literature review will be thorough and will include the work done directly on modelling downhole seismic sources and the comparatively larger amount of work done on modelling sources for acoustic logging purposes which is directly applicable. Different authors publishing work on seismic sources have made widely different symmetry assumptions ranging from no symmetry to axisymmetry to symmetry along the z axis. These differences hamper the ability to directly compare results between the different treatments. Compounding the differences in symmetry are the use of different time dependencies ([superscript -iwl], [superscript iwl]) and the use of different Hankel function or modified Bessel function strategies. Therefore, the mathematical fundamentals of wave propagation in a borehole from the different symmetry systems are presented here in a consistent notation and are related to each other and treatments in the literature to help eliminate duplication of effort. Finally, wave propagation outside a borehole is examined using synthetic seismograms. For the synthetic seismograms, a point source inside the borehole is used as a source and the synthetics are calculated using the discrete wavenumber method. The synthetic seismograms are measured along vertical arrays of point receivers placed outside the borehole and for lithologies of Pierre shale, Solenhofen limestone, and Berea sandstone. The method and the resulting seismograms are outlined in this paper along with a brief description of the discrete wavenumber technique.Massachusetts Institute of Technology. Full Waveform Acoustic Logging Consortiu

Analytical Studies of Boundary Layer Generated Aircraft Interior Noise

An analysis is made of the "interior noise" produced by high, subsonic turbulent flow over a thin elastic plate partitioned into "panels" by straight edges transverse to the mean flow direction. This configuration models a section of an aircraft fuselage that may be regarded as locally flat. The analytical problem can be solved in closed form to represent the acoustic radiation in terms of prescribed turbulent boundary layer pressure fluctuations. Two cases are considered: (i) the production of sound at an isolated panel edge (i.e., in the approximation in which the correlation between sound and vibrations generated at neighboring edges is neglected), and (ii) the sound generated by a periodic arrangement of identical panels. The latter problem is amenable to exact analytical treatment provided the panel edge conditions are the same for all panels. Detailed predictions of the interior noise depend on a knowledge of the turbulent boundary layer wall pressure spectrum, and are given here in terms of an empirical spectrum proposed by Laganelli and Wolfe. It is expected that these analytical representations of the sound generated by simplified models of fluid-structure interactions can used to validate more general numerical schemes

Numerical simulation of separated flows

A new numerical method, based on the Vortex Method, for the simulation of two-dimensional separated flows, was developed and tested on a wide range of gases. The fluid is incompressible and the Reynolds number is high. A rigorous analytical basis for the representation of the Navier-Stokes equation in terms of the vorticity is used. An equation for the control of circulation around each body is included. An inviscid outer flow (computed by the Vortex Method) was coupled with a viscous boundary layer flow (computed by an Eulerian method). This version of the Vortex Method treats bodies of arbitrary shape, and accurately computes the pressure and shear stress at the solid boundary. These two quantities reflect the structure of the boundary layer. Several versions of the method are presented and applied to various problems, most of which have massive separation. Comparison of its results with other results, generally experimental, demonstrates the reliability and the general accuracy of the new method, with little dependence on empirical parameters. Many of the complex features of the flow past a circular cylinder, over a wide range of Reynolds numbers, are correctly reproduced

Theory of minimum effort control

Optimum control theory formulations for solving problems in optimum guidance for interplanetary manned space flight mission

Two dimensional turbulence in inviscid fluids or guiding center plasmas

Analytic theory for two-dimensional turbulent equilibria for the inviscid Navier-Stokes equations is examined mathematically. Application of the technique to electrostatic guiding center plasma is discussed. A good fit is demonstrated for the approach to a predicted energy per Fourier mode obtained from a two-temperature canonical ensemble. Negative as well as positive temperature regimes are explored. Fluctuations about the mean energy per mode also compare well with theory. In the regime of alpha less than zero, beta greater than zero, with the minimum value of alpha plus beta times k squared near zero, contour plots of the stream function reveal macroscopic vortex structures similar to those seen previously in discrete vortex simulations. Eulerian direct interaction equations, which can be used to follow the approach to inviscid equilibrium, are derived