Rayleigh's problem at low Mach numbers based on kinetic theory.
Rayleigh problem solution and accuracy and utility of discrete ordinate method for time dependent problems as applied to Couette flow problems
RAYLEIGH NUMBER↗
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Performance of a Radial-inlet Impeller Designed on the Basis of Two-dimensional-flow Theory for an Infinite Number of Blades
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Johnsen, I A↗
Mean-field theory of spin-glasses with finite coordination number
The mean-field theory of dilute spin-glasses is studied in the limit where the average coordination number is finite. The zero-temperature phase diagram is calculated and the relationship between the spin-glass phase and the percolation transition is discussed. The present formalism is applicable also to graph optimization problems.
Kanter, I.↗
A comparison between an existing propeller noise theory and wind tunnel data
The noise of three supersonic helical tip speed propellers was compared with the noise predicted by an existing noise theory. Comparisons of the peak blade passage tones showed fairly good agreement beween theory and experiment at the lowest helical tip Mach numbers tested, 0.86 and 1.00, while at higher numbers, the theory predicted higher noise levels than measured. When the differences among the propellers were considered the theory and measurement showed fairly good agreement. Directivity measurements in general showed that the measured blade passage tone data peaked further downstream than the theory predicted. At the cruise design condition the harmonics appeared to fall off faster in the data than the theory indicated.
Dittmar, J. H.↗
Fundamental equations of the theory of shells consisting of an arbitrary number of anisotropic layers
Equations of theory of shells consisting of several anisotropic layers
ANISOTROPIC SHELL↗
Analytic theory for the selection of 2-D needle crystal at arbitrary Peclet number
An accurate analytic theory is presented for the velocity selection of a two-dimensional needle crystal for arbitrary Peclet number for small values of the surface tension parameter. The velocity selection is caused by the effect of transcendentally small terms which are determined by analytic continuation to the complex plane and analysis of nonlinear equations. The work supports the general conclusion of previous small Peclet number analytical results of other investigators, though there are some discrepancies in details. It also addresses questions raised on the validity of selection theory owing to assumptions made on shape corrections at large distances from the tip.
Tanveer, Saleh↗
The Mach number of the cosmic flow - A critical test for current theories
A new cosmological, self-contained test using the ratio of mean velocity and the velocity dispersion in the mean flow frame of a group of test objects is presented. To allow comparison with linear theory, the velocity field must first be smoothed on a suitable scale. In the context of linear perturbation theory, the Mach number M(R) which measures the ratio of power on scales larger than to scales smaller than the patch size R, is independent of the perturbation amplitude and also of bias. An apparent inconsistency is found for standard values of power-law index n = 1 and cosmological density parameter Omega = 1, when comparing values of M(R) predicted by popular models with tentative available observations. Nonstandard models based on adiabatic perturbations with either negative n or small Omega value also fail, due to creation of unacceptably large microwave background fluctuations.
Ostriker, Jeremiah P.↗
A finite Reynolds number approach for the prediction of boundary layer receptivity in localized regions
Previous theoretical work on the boundary layer receptivity problem has utilized large Reynolds number asymptotic theories, thus being limited to a narrow part of the frequency - Reynolds number domain. An alternative approach is presented for the prediction of localized instability generation which has a general applicability, and also accounts for finite Reynolds number effects. This approach is illustrated for the case of Tollmien-Schlichting wave generation in a Blasius boundary layer due to the interaction of a free stream acoustic wave with a region of short scale variation in the surface boundary condition. The specific types of wall inhomogeneities studied are: regions of short scale variations in wall suction, wall admittance, and wall geometry (roughness). Extensive comparison is made between the results of the finite Reynolds number approach and previous asymptotic predictions, which also suggests an alternative way of using the latter at Reynolds numbers of interest in practice.
Choudhari, Meelan↗
A finite Reynolds-number approach for the prediction of boundary-layer receptivity in localized regions
Previous theoretical work on the boundary layer receptivity problem has utilized large Reynolds number asymptotic theories, thus being limited to a narrow part of the frequency-Reynolds number domain. An alternative approach is presented for the prediction of localized instability generation which has a general applicability, and also accounts for finite Reynolds number effects. This approach is illustrated for the case of Tollmien-Schlichting wave generation in a Blasius boundary layer due to the interaction of a free stream acoustic wave with a region of short scale variation in the surface boundary condition. The specific types of wall inhomogeneities studied are: regions of short scale variations in wall suction, wall admittance, and wall geometry (roughness). Extensive comparison is made between the results of the finite Reynolds number approach and previous asymptotic predictions, which also suggests an alternative way of using the latter at Reynolds numbers of interest in practice.
Choudhari, Meelan↗
Analytic theory for the selection of a two-dimensional needle crystal at arbitrary Peclet number
An accurate analytic theory is presented for the velocity selection of a two-dimensional needle crystal for arbitrary Peclet number for small values of the surface tension parameter. The velocity selection is caused by the effect of transcendentally small terms which are determined by analytic continuation to the complex plane and analysis of nonlinear equations. The work supports the general conclusion of previous small Peclet number analytical results of other investigators, though there are some discrepancies in details. It also addresses questions raised on the validity of selection theory owing to assumptions made on shape corrections at large distances from the tip.
Tanveer, S.↗
Direct measurements of turbulent skin friction on a nonadiabactic flat plate at Mach number 6.5 and comparisons with eight theories
Turbulent skin friction on nonadiabatic flat plate at Mach number 6.5
Hopkins, E. J.↗
Mach number scaling of helicopter rotor blade/vortex interaction noise
A parametric study of model helicopter rotor blade slap due to blade vortex interaction (BVI) was conducted in a 5 by 7.5-foot anechoic wind tunnel using model helicopter rotors with two, three, and four blades. The results were compared with a previously developed Mach number scaling theory. Three- and four-bladed rotor configurations were found to show very good agreement with the Mach number to the sixth power law for all conditions tested. A reduction of conditions for which BVI blade slap is detected was observed for three-bladed rotors when compared to the two-bladed baseline. The advance ratio boundaries of the four-bladed rotor exhibited an angular dependence not present for the two-bladed configuration. The upper limits for the advance ratio boundaries of the four-bladed rotors increased with increasing rotational speed.
Leighton, Kenneth P.↗
Variability of rainfall over small areas
A preliminary investigation was made to determine estimates of the number of raingauges needed in order to measure the variability of rainfall in time and space over small areas (approximately 40 sq miles). The literature on rainfall variability was examined and the types of empirical relationships used to relate rainfall variations to meteorological and catchment-area characteristics were considered. Relations between the coefficient of variation and areal-mean rainfall and area have been used by several investigators. These parameters seemed reasonable ones to use in any future study of rainfall variations. From a knowledge of an appropriate coefficient of variation (determined by the above-mentioned relations) the number rain gauges needed for the precise determination of areal-mean rainfall may be calculated by statistical estimation theory. The number gauges needed to measure the coefficient of variation over a 40 sq miles area, with varying degrees of error, was found to range from 264 (10% error, mean precipitation = 0.1 in) to about 2 (100% error, mean precipitation = 0.1 in).
Runnels, R. C.↗
A theory for the core flow of leading-edge vortices
Separation-induced leading-edge vortices can dominate the flow about slender wings at moderate to high angles of attack, often with favorable aerodynamic effects. However, at the high angles of attack which are desirable for takeoff and landing as well as subsonic-transonic maneuver the vortices can breakdown or burst in the vicinity of the aircraft causing many adverse effects; these include lift loss, pitchup, and buffet. The flow in the core of leading-edge vortices is generally affiliated with the vortex breakdown phenomenon. A theory is presented for the flow in the core of separation-induced, leading-edge vortices at practical Reynolds numbers. The theory is based on matching inner and outer representations of the vortex. The inner representation models continuously distributed vorticity and includes an asymptotic viscous subcore. The outer representation models concentrated spiral sheets of vorticity and is fully three dimensional. A parameter is identified which closely tracks the vortex breakdown stability boundary for delta, arrow, and diamond wings.
Luckring, James M.↗
Natural vibrations of laminated anisotropic plates using three-dimensional elasticity theory
The paper contains a description of the three-dimensional elasticity equations and the associated finite element model for natural vibrations of laminated anisotropic rectangular plates. The numerical results for natural frequencies are compared with those obtained by a shear deformable plate theory. A number of cross-ply and angle-ply rectangular plates are analyzed for natural frequencies. For relatively thick plates, the shear deformable-plate theory element predicts frequencies higher than those predicted by the three-dimensional elasticity theory element.
Reddy, J. N.↗
Numerical results in the statistical theory of thermal turbulence
Several statistical theories of turbulence are applied to thermal convection problem, and are compared in a series of numerical calculations. Results are presented for both the case of very large and very small Prandtl numbers, and for moderate Rayleigh numbers. The theories compared are the direct-interaction approximation, the self-consistent field approximation, the quasi-linear approximation, the quasi-normal approximation, and a 'Markovianized' quasi-normal approximation. Results for these theories are then compared with some simple exact solutions to the statistical problem. The results indicate that the direct-interaction and the self-consistent field method give satisfactory results at all Rayleigh numbers investigated, whereas the procedures based on the quasi-normal approximation give sensible results only at small Rayleigh numbers.
Herring, J. R.↗
Communication training for aircrews: A review of theoretical and pragmatic aspects of training program design
This study is the final report of a project studying methods of communications training applicable to both civilian and military aviation personnel, including multiperson teams or single pilot fixed wing or rotary wing aircraft. A review is provided of a number of theories proposed as relevant for producing training materials for improved communications. Criteria are given for evaluating the applicability of training programs to the aviation environment, and these criteria are applied to United Airlines' Resources Management Training, as well as to a number of commercially available general purpose training programs. The report considers in detail assertiveness training and grid management training, examining their theoretical background and attempts made to validate their effectiveness. It was found that there are substantive difficulties in assessing the effectiveness of both training programs, as well as problems with the theories underlying them. However, because the aviation environment offers unique advantages for studying the effectiveness of communications training, recommendations are made on the design of appropriate training programs and on procedures that might be used to validate them.
Linde, Charlotte↗
Using dynamo theory to predict the sunspot number during solar cycle 21
On physical grounds it is suggested that the polar field strength of the sun near a solar minimum is closely related to the solar activity of the following cycle. Four methods of estimating the polar magnetic field strength of the sun near solar minimum are employed to provide an estimate of the yearly mean sunspot number of cycle 21 at solar maximum of 140 + or - 20. This estimate may be considered a first-order attempt to predict the cycle activity using one parameter of physical importance based upon dynamo theory.
Schatten, K. H.↗