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Several theories of velocity fluctuations in the atmosphere are discussed in the context of the horizontal wavenumber power spectral density (PSD). The main purpose of this report is to provide an experimental method to decide the question of which of these various theories are viable. The presently existing explanations of this PSD fall into the following categories: (a) quasi-two-dimensional turbulence theories as proposed by Gage and by Lilly; (b)theories of waves in cascade as proposed by Dewan; (c) "separable" gravity wave theories which explain horizontal wavenumber PSD slopes in terms of vertical wavenumber and temporal frequency PSD slopes, as proposed by Gardner et al., and (d) the diffusive filtering theory, as proposed by Gardner. The experimental test proposed in this report is based on the horizontal wavenumber PSD observations of Nastrom and of Bacmeister et al, who reported that, under certain circumstances, this PSD exhibited a change of slope (going from -5/3 to -3) as the wavenumber increased.

The saturated-cascade theory for atmospheric gravity wave (GW) spectra combines the physics of wave saturation with that of wave-wave interactions (the latter being in the form of a cascade). This theory successfully explained the slopes of 11 classes of measured GW spectra, the variability of some spectra compared to the quasi-universality of certain other spectra, and finally, the observed association between wavelength and wave period in individual wave observations. Unfortunately, the cascade properties in this theory have heretofore received only indirect confirmation in spite of the fact that direct evidence could be obtained by experimental means using today's technology. In this report, the available direct experimental evidence for the wave cascade that is now available in the papers by Nastrom et al. and Bacmeister et al. is examined, and further tests along these lines are suggested.

The MAPSTAR program was both a theoretical and experimental investigation of airglow structure and its causes. We found that the most important cause of the structures is atmospheric gravity waves, and that thunderstorms are a clearly identified source of the waves responsible for such structure. We also studied many related issues. In addition, two new instruments were designed and fabricated during this program. These were the MAPSTAR infrared Michelson interferometer and the MAPSTAR radar imaging Doppler interferometer. The latter instrument has played the crucial role in removing discrepancies between different methods of radar wind profiling. Structures investigated under MAPSTAR give rise to system clutter; thus having direct impact upon Air Force surveillance operations from space. (AN)

Internal gravity waves are present in both the ocean and atmosphere. The oceanic gravity wave power spectra have been modeled semi-empirically by Garrett and Munk (1972, 1975) and shown to have 'universal' properties. Their model seems to be useful for atmospheric waves. Recently a similitude type of 'saturation' model for vertical wave number horizontal velocity fluctuation spectra has met with empirical support in the atmosphere. The present paper employs a further similitude argument related to 'cascade' properties which would apply to the frequency and horizontal wave number spectra. Testable consequences are exhibited. If validated the models would provide useful insight into the physics of these waves., Pub. in Geophysical Research Letters, v18 n8, p1473- 1476.

In order to estimate the rate of vertical transport due to turbulence in the stratosphere, it is necessary to know the degree of mixing that takes place in 'Kelvin-Helmholtz billow events.' This is estimated by means of a discrete model and the results are compared with published experimental observations. From these considerations it is concluded that a very large degree of mixing probably takes place in such events, and that, therefore, one must use the relation between the bulk vertical eddy diffusivity and layer diffusivity originally proposed by Rosenberg and Dewan instead of the simple one usually employed.

This paper reviews the estimates to date of the vertical 'effective diffusion coefficient' for stratospheric small scale turbulence transport, KB. These estimates range (in order of magnitude) from 1.0 sq. meter/s to 0.01 sq. meter/s, that is to say from a value which would make turbulence a dominant factor in stratospheric transport to a value which would make it totally insignificant. Such a large range implies much ignorance in this subject. The various techniques are closely examined and the unanswered experimental questions are exhibited. The conclusion is reached that more experimental work needs to be done before one has a reliable estimate for KB.

A self-consistent method of characterizing vertical turbulent transport by means of a diffusion parameter is demonstrated for the extremely inhomogeneous case of layered turbulence in a stratified fluid. Between the horizontal turbulent layers, horizontal laminar flow is assumed to occur, and molecular diffusion is ignored. The layers are assumed to occur at random heights with random thickness. An analogy is made between the process of random mixing layers and the finite difference representation of the diffusion equation. It is demonstrated by means of a series of digital computer experiments that, in the case where total mixing takes place within the turbulent layers, the diffusion parameter herein developed is the valid one to use (in contrast to 'eddy diffusivity'). The relation between this inhomogeneous diffusion parameter and practical experimental measurements is given. The motive behind this investigation involves vertical transport of pollution in the environment in general and in the stratosphere in particular.

Vertical transport in the stratosphere occurs by many processes and the question of the relative importance of stratified turbulence is considered in the context of a 'vertical stack model' described in a previous report. The 'vertical stack model' was designed to estimate the effect of intermittent turbulent layers (separated by essentially laminar flow) and it is here examined in some detail. In particular, a number of less obvious implications are discussed and a list of experimental tests of the model is suggested. It is concluded that the rate of turbulence for vertical transport in the stratosphere remains an open question.

There are many situations where a great increase in the resolution of power spectral densities, PSD's, would solve important problems. The problem areas range from radar, speech compression, seismic signal processing, to spectral analysis of optical signals. The maximum entropy method (MEM) can, under certain circumstances, provide an order of magnitude increase in resolution over conventional techniques. The fundamental concepts and mathematical background are given and, most importantly, the peculiarities and new features introduced by the MEM technique are explained. Some signals are good candidates for this technique while others are not; thus, methods are described to distinguish between the two. After the techniques to obtain the MEM-PSD are explained, an application to Fourier Spectroscopy is given to illustrate the results (as compared to conventional means). This review employs certain features to make the MEM approach accessible to those without previous knowledge about it. These features include: a short history of the PSD which describes the evolution over time of the basic concepts; a discussion of the higher principle of maximum entropy in the context of probability theory; a simple introduction to the Z-transform and how it introduces the basic spectral line shape of the MEM-PSD as well as other peculiarities of the method which distinguish it from the conventional approach; the physics behind the reflection coefficients which are introduced by MEM; and an extensive annotated bibliography which should make the literature available.

What are the theoretical and experimental physical differences between waves and turbulence? The motivation behind this question is related to the practical problems associated with laser beam propagation and pollution transport in the atmosphere. Because turbulence causes mixing and waves do not, one must not regard turbulence as a field of random waves. The power density spectrum of velocity fluctuations, when taken along, cannot be used to distinguish between waves and turbulence. Its physical interpretation can differ radically depending upon which type of motion is involved. Two approaches are used here to differentiate theoretically and experimentally between waves and turbulence. The first involves the degree of interaction between modes. The second approach depends on the mixing property of turbulence.

This report is a tutorial on the effects of atmospheric turbulence upon systems which rely upon the propagation of LASER beams. In addition to providing a simplified presentation of turbulence theory and optical effects, it describes the state of the art of the new technique of radiosonde estimation of index of refraction fluctuations. suggestions are given for future research which will help to answer current Air Force needs. The feasibility of some laser systems will depend upon the value of r sub o, the coherence length (which is related to C sub n sq. which in turn is related to the degree of turbulence). At present, the statistics of r sub o are inadequate. (Author)

This paper is motivated by the requirement to improve understanding of vertical motion of pollutants in the stratosphere. One method to estimate vertical transport due to the effects of turbulence is by means of the effective diffusivity coefficient. To calculate this parameter, it is often necessary to know the value of epsilon, the rate of turbulent dissipation. This parameter, epsilon, is also important to know in the context of the global numerical stratospheric simulation models now being created for environmental assessment purposes.

Special relativity is a subject which seems to defy common sense. The theory is presented from a new point of view as an attempt to help the reader acquire an understanding that relies not only on mathematical consistency but on consistency with common sense as well. The principle of relativity in the derivation of the Lorentz Transformations is replaced by three postulates which are directly connected with certain experiments; their epistemological and physical significance is then exposed. Gedanken experiments are employed to show that the apparent inconsistencies are actually non-contradictory from the points of view of all inertial observers. (Author)

The problem of a thermally stratified compressible fluid on a rotating sphere with gravitation is discussed. An exact solution to the nonlinear Euler equations pertaining to this problem, which was recently obtained by H. E. Moses, is physically explained. The work represents a contribution toward a theoretical understanding of the motions and forces in the atmosphere, the environment in which the Air Force operates. (Modified author abstract)

Generalized harmonic analysis has been applied in many fields, and has become the basis of statistical communication theory. This paper introduces another generalization of this technique, with the specific intention of testing the nature of nonlinear interaction in time series data. The nonlinear cross-spectrum developed is illustrated with examples from meteorology and neuroelectric signals. (Author)

The adaptive behavior of higher animals is regarded as implying a spontaneous self-reprogramming process taking place in the brain. This process is assumed to be specifically organized to prepare the animal for its current needs. Secondly, it is then hypothesized that an important part of this takes place during sleep. Then the hypothesis is made more definite by assuming that Stage I-REM sleep (a stage of sleep correlated with subjective dreaming) plays an absolutely fundamental role in this process (that is, it is necessary and sufficient for programming to take place). The consequences of this oversimplified postulate are enumerated in the form of experimental predictions (some of which have already received dramatic confirmation). The main content of this report deals with experimental predictions and theoretical implications which fall into six categories: (1) Physical aspects, (2) memory aspects, (3) perceptual and sensory-motor aspects, (4) the role of drives and emotions, (5) homeostatic and biorhythmic aspects, and (6) effects of breakdown of programming. (Author)

Asynchronous excitation (AE) by means of an asynchronous input that effectively modifies a hard oscillation so that it becomes soft, is investigated at the mathematical and physical levels. Computer simulation is used for displaying the phenomenon. It is also shown that a second input in the neighborhood of the oscillator's natural frequency phase-locks the AE oscillation and causes periodic pulling just outside the detuning zone. (Author)

Ball lightning has until this time defied physical explanation. This report summarizes the requirements that must be satisfied by any valid theory, reviews and evaluates previous theories, and evaluates the new theory of Finkelstein and Rubenstein developed under an AFCRL-monitored grant. It is concluded that the latter theory is the only promising one to date but that even this theory needs to be modified. A modification is proposed which would remove the remaining objections and it is suggested that experiments rather than further theoretical development will constitute the next decisive step. Previous theories discussed are: combustion, confined plasma, dust, electromagnetic radiation, cosmic ray, and quantum mechanics.