Orthogonality, positive operators, and the frequency-power formulas
Orthogonality and positive operators on space of almost periodic and quasi-periodic functions, using frequency-power formulas
Skoog, R. A.↗
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FORTRAN program for generating a two-dimensional orthogonal mesh between two arbitrary boundaries
Computer program is described which computes and plots coordinates for two-dimensional orthogonal mesh for channel containing solid body, about which flow passes and which spans channel from one wall to the other.
Mcnally, W. D.↗
A class of orthogonal nonrecursive binomial filters.
The time- and frequency-domain properties of the orthogonal binomial sequences are presented. It is shown that these sequences, or digital filters based on them, can be generated using adders and delay elements only. The frequency-domain behavior of these nonrecursive binomial filters suggests a number of applications as low-pass Gaussian filters or as inexpensive bandpass filters.
Haddad, R. A.↗
Analysis of chromatograph systems using orthogonal collocation
Research is generating fundamental engineering design techniques and concepts for the chromatographic separator of a chemical analysis system for an unmanned, Martian roving vehicle. A chromatograph model is developed which incorporates previously neglected transport mechanisms. The numerical technique of orthogonal collocation is studied. To establish the utility of the method, three models of increasing complexity are considered, the latter two being limiting cases of the derived model: (1) a simple, diffusion-convection model; (2) a rate of adsorption limited, inter-intraparticle model; and (3) an inter-intraparticle model with negligible mass transfer resistance.
Woodrow, P. T.↗
Multibeam-antenna feed system to isolate orthogonally polarized beams
System is polarization tracker and comprises variable polarizer, polarization control, and receiver servo loop. System simultaneously receives desired signal and undesired signal which are approximately orthogonal. They can be either paired as left and right circular polarizations or as cross-linear polarizations.
Ohlson, J. E.↗
Method of Characteristics Calculations and Computer Code for Materials with Arbitrary Equations of State and Using Orthogonal Polynomial Least Square Surface Fits
A numerical scheme using the method of characteristics to calculate the flow properties and pressures behind decaying shock waves for materials under hypervelocity impact is developed. Time-consuming double interpolation subroutines are replaced by a technique based on orthogonal polynomial least square surface fits. Typical calculated results are given and compared with the double interpolation results. The complete computer program is included.
Chang, T. S.↗
Forebody and afterbody solutions of the Navier-Stokes equations for supersonic flow over blunt bodies in a generalized orthogonal coordinate system
A coordinate transformation, which can approximate many different two-dimensional and axisymmetric body shapes with an analytic function, is used as a basis for solving the Navier-Stokes equations for the purpose of predicting 0 deg angle of attack supersonic flow fields. The transformation defines a curvilinear, orthogonal coordinate system in which coordinate lines are perpendicular to the body and the body is defined by one coordinate line. This system is mapped in to a rectangular computational domain in which the governing flow field equations are solved numerically. Advantages of this technique are that the specification of boundary conditions are simplified and, most importantly, the entire flow field can be obtained, including flow in the wake. Good agreement has been obtained with experimental data for pressure distributions, density distributions, and heat transfer over spheres and cylinders in supersonic flow. Approximations to the Viking aeroshell and to a candidate Jupiter probe are presented and flow fields over these shapes are calculated.
Gnoffo, P. A.↗
Estimates of oceanic surface wind speed and direction using orthogonal beam scatterometer measurements and comparison of recent sea scattering theories
The wind direction properties of radar backscatter from the sea were empirically modelled using a cosine Fourier series through the 4th harmonic in wind direction (referenced to upwind). A comparison with 1975 JONSWAP (Joint North Sea Wave Project) scatterometer data, at incidence angles of 40 and 65, indicates that effects to third and fourth harmonics are negligible. Another important result is that the Fourier coefficients through the second harmonic are related to wind speed by a power law expression. A technique is also proposed to estimate the wind speed and direction over the ocean from two orthogonal scattering measurements. A comparison between two different types of sea scatter theories, one type presented by the work of Wright and the other by that of Chan and Fung, was made with recent scatterometer measurements. It demonstrates that a complete scattering model must include some provisions for the anisotropic characteristics of the sea scatter, and use a sea spectrum which depends upon wind speed.
Moore, R. K.↗
Equations of motion and two-equation turbulence model for plane or axisymmetric turbulent flows in body-oriented orthogonal curvilinear coordinates and mass-averaged dependent variables
The full Navier-Stokes time-dependent, compressible, turbulent, mean-flow equations in mass-averaged variables for plane or axisymmetric flow are presented. The equations are derived in a body-oriented, orthogonal, curvilinear coordinate system. Turbulence is modelled by a system of two equations for mass-averaged turbulent kinetic energy and dissipation rate proposed. These equations are rederived and some new features are discussed. A system of second order boundary layer equations is then derived which includes the effects of longitudinal curvature and the normal pressure gradient. The Wilcox and Chambers approach is used in considering effects of streamline curvature on turbulence phenomena in turbulent boundary layer type flows. Their two-equation turbulence model with curvature terms are rederived for the cases considered in the present report. The derived system equations serves as a basis for an investigation of problems where streamline curvature is of the order of the characteristic length in the longitudinal direction.
Sislian, J. P.↗
Complete supersonic flowfields over blunt bodies in a generalized orthogonal coordinate system
A general orthogonal coordinate system is used to describe various axisymmetric and two-dimensional shapes. Close approximations to planetary probe configurations are possible. The full Navier-Stokes equations are discretized in this coordinate system in a manner based on Allen and Cheng's numerical procedure. The blow shock is treated as a discontinuity which floats between grid points. Completely coupled flows over the forebody, base, and near wake were calculated over a cylinder, sphere, and an approximation to the Viking Aeroshell. Some problem areas in determining the base flow for increasing Reynolds number are discussed. In particular, it is found that the mean free path of the fluid near the wall immediately below the corner of the Viking Aeroshell, which experiences a severe expansion, can become greater than the local mesh size required to resolve the boundary layer in the forebody.
Gnoffo, P. A.↗
Elastic stability of superplastically formed/diffusion-bonded orthogonally corrugated core sandwich plates
The paper concerns the elastic buckling behavior of a newly developed superplastically formed/diffusion-bonded (SPF/DB) orthogonally corrugated core sandwich plate. Uniaxial buckling loads were calculated for this type of sandwich plate with simply supported edges by using orthotropic sandwich plate theory. The buckling behavior of this sandwich plate was then compared with that of an SPF/DB unidirectionally corrugated core sandwich plate under conditions of equal structural density. It was found that the buckling load for the former was considerably higher than that of the latter.
Ko, W. L.↗
Improved orthogonality check for measured modes
A method is proposed for performing an orthogonality check for normal modes derived from ground vibration testing. The method utilizes partitioned mass and stiffness matrices for a linear undamped representation of a structure. The normalization of the modes by the proposed method inherently includes the effects of significant displacements which were not measured; and the method may allow the use of fewer measurement points than would be necessary with the conventional method.
Berman, A.↗
Numerical generation of two-dimensional orthogonal curvilinear coordinates in an Euclidean space
A noniterative method for the numerical generation of orthogonal curvilinear coordinates for plane annular regions between two arbitrary smooth closed curves was developed. The basic generating equation is the Gaussian equation for an Euclidean space which is solved analytically. The method is applied in many cases and these test results demonstrate that the proposed method can be readily applied to a wide variety of problems. The method can also be used for simply connected regions only by obtaining the solution of the linear equation under the changed boundary conditions.
Warsi, Z. U. A.↗
Viscous compressible flow about blunt bodies using a numerically generated orthogonal coordinate system
A numerical solution to the Navier-Stokes equations was obtained for blunt axisymmetric entry bodies of arbitrary shape in supersonic flow. These equations are solved on a finite difference mesh obtained from a simple numerical technique which generates orthogonal coordinates between arbitrary boundaries. The governing equations are solved in time dependent form using Stetter's improved stability three step predictor corrector method. For the present application, the metric coefficients were obtained numerically using fourth order accurate, finite difference relations and proved to be totally reliable for the highly stretched mesh used to resolve the thin viscous boundary layer. Solutions are obtained for a range of blunt body nose shapes including concavities.
Graves, R. A., Jr.↗
Torque generated by orthogonal acoustic waves - Theory
An analytical calculation of the torque generated by orthogonal waves is reported. This torque is a result of a viscous effect, rather than the Bernoulli effect as in Rayleigh's torque. The agreement between the reported experimental values and this calculation is excellent.
Busse, F. H.↗
Sampling errors in the estimation of empirical orthogonal functions
Empirical Orthogonal Functions (EOF's), eigenvectors of the spatial cross-covariance matrix of a meteorological field, are reviewed with special attention given to the necessary weighting factors for gridded data and the sampling errors incurred when too small a sample is available. The geographical shape of an EOF shows large intersample variability when its associated eigenvalue is 'close' to a neighboring one. A rule of thumb indicating when an EOF is likely to be subject to large sampling fluctuations is presented. An explicit example, based on the statistics of the 500 mb geopotential height field, displays large intersample variability in the EOF's for sample sizes of a few hundred independent realizations, a size seldom exceeded by meteorological data sets.
North, G. R.↗
On orthogonal expansions of the space of vector functions which are square-summable over a given domain and the vector analysis operators
The Hilbert space L2(omega) of vector functions is studied. A breakdown of L2(omega) into orthogonal subspaces is discussed and the properties of the operators for projection onto these subspaces are investigated from the standpoint of preserving the differential properties of the vectors being projected. Finally, the properties of the operators are examined.
Bykhovskiy, E. B.↗
Structural performance of orthogonal tetrahedral truss Space-Station configurations
Two 150 kW space station configurations constructed with the orthogonal tetrahedral truss concept are described. One space station consists of a large central platform and two rotating solar wing arrays and the other consists of a long central keel with two rotating arrays. The dynamic characteristics of each configuration are obtained with and without nonstructural components present. The variation in frequencies and mass moments of inertia due to rotation of the two solar wing arrays are given for the long keel space station configuration. The structural performance of the solar wing array is assessed for cases where individual critical struts fail in the array support truss.
Dorsey, J. T.↗