Theory of radiative transfer in inhomogeneous atmospheres. II
Perturbation method developed for linearizing nonlinear singular equation for inhomogeneous stratified atmosphere H-function in theory of radiative transfer
Abhyankar, K. D.↗
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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Effect of pressure fluctuations on laminar film boiling
Time dependent pressure fluctuations effect on laminar film pool boiling on vertical flat plate by perturbation method to predict heat transfer
Burmeister, L. C.↗
Principles of celestial mechanics
Book on celestial mechanics covering perturbation methods, two body problems, astronomical coordinates, orbital mechanics, satellite rotation, gravitational effects, etc
Fitzpatrick, P. M.↗
Propagation of coherent waves in a warm turbulent magnetoplasma
Coherent wave propagation in warm turbulent plasma, using perturbation method for wave dispersion
Liu, C. H.↗
Perturbation solution of a hyperbolic equation governing longitudinal wave propagation in certain nonuniform bars
Longitudinal wave propagation in variable section bars, solving hyperbolic equation of motion by perturbation method
Davis, R. T.↗
Attenuation of plane wave and higher order mode sound propagation in lined ducts
Perturbation method to obtain analytical expressions for attenuation of plane wave sound propagation in lined ducts
Doak, P. E.↗
Parametric excitation of a plasma
Plasma waves parametric excitation by external electric field, using perturbation method of multitime scales
Chen, C. S.↗
Optimization of non-linear systems with inequality constraints explicitly containing the control
Lifting reentry vehicle two dimensional motion optimization with inequality constraints explicitly containing control by perturbation method
Lastman, G. J.↗
Amplitude dispersion and stability of dissipative weakly nonlinear waves
Amplitude dispersion and stability of dissipative weakly nonlinear waves determined by perturbation method
Cap, F. F.↗
Parametric excitation in an inhomogeneous plasma
Parametric excitation of transverse waves in inhomogeneous electron plasma driven by oscillating electric field, using multitime perturbation method
Chen, C. S.↗
Analytical Lunar Ephemeris - Progress report
Gravitational lunar theory high order solution for geophysical relevance, discussing perturbation methods and computer analyzed ephemeris time
Deprit, A.↗
A theoretical study of radar return and radiometric emission from the sea
The applicability of the various electromagnetic models of scattering from the ocean are reviewed. These models include the small perturbation method, the geometric optics solution, the composite model, and the exact integral equation solution. The restrictions on the electromagnetic models are discussed.
Peake, W. H.↗
A note on 'The main problem of satellite theory for small eccentricities, by A. Deprit and A. Rom, 1970.'
Criticism of Deprit and Rom's (1970) extension of Brouwer's (1959) first-order satellite theory to the third order in J sub 2. It is noted that Deprit and Rom's theory suffers from the drawback that the perturbations of all orders are expressed as infinite power series in the eccentricity e. It is demonstrated that Deprit and Rom's reported failure to extend Brouwer's theory to the second order in a closed form by means of Lie transforms is due to an oversight and is not caused by difficulties inherent in the problem or in the particular perturbation method used.
Aksnes, K.↗
Non-linear flap-lag dynamics of hingeless helicopter blades in hover and in forward flight.
The aeroelastic instability of the coupled nonlinear flap-lag motion of a torsionally rigid helicopter blade is treated by using the perturbation method in multiple time scales. The nonlinearities present in the equations are those arising from the inclusion of moderately large deflections in the inertia and aerodynamic loading terms. The stability boundaries, amplitudes of nonlinear response, and conditions for existence of limit cycles are obtained analytically. Thus the different roles played by the forcing, parametric excitation, and nonlinear coupling in affecting the solution can be easily identified. Numerical results illustrating the behavior of the blade are presented.
Friedmann, P.↗
The radiative effect of aerosols in the earth's atmosphere
A modified two-flux approximation is employed to compute the transfer of radiation in a finite, inhomogeneous, turbid atmosphere. A perturbation technique is developed to allow the treatment of nongray gaseous absorption with multiple scattering. The perturbation method, which employs a backscatter factor as a parameter, can be used with anisotropic particle scattering as well as Rayleigh scattering. This method is used to study the effect of aerosols on radiative solar heating and infrared cooling as well as the radiative-convective temperature distribution in the earth's atmosphere. It is found that the effect of aerosols in the infrared cannot be neglected; while in the visible, the effect can be of the same order as that due to absorption by water vapor. For a high surface albedo (greater than 0.30) heating of the earth-atmosphere system results due to the presence of aerosols. The aerosols also reduce the amount of convection needed to maintain a stable atmosphere. For the case of a dense haze a temperature inversion is found to exist close to the ground.
Wang, W.-C.↗
A theory of wave scatter from an inhomogeneous medium with a slightly rough boundary and its application to sea ice
An analytical theory of electromagnetic wave scattering from an inhomogeneous medium with a slightly rough boundary surface is formulated. The inhomogeneity in the medium is assumed to vary continuously in the vertical direction and to have a small random variation in the horizontal direction. The medium is assumed to consist of two layers. Maxwell's equations are solved by using the small perturbation method together with Fourier transform technique. The resulting differential equations are solved by using WKB and variation of parameter methods. Field amplitudes in each medium are determined by taking boundary conditions into account. The expressions for first order polarized radar backscatter cross-section are obtained. An attempt is made to apply the developed theory to compute sea ice scatter. Numerical calculations are performed for polarized radar backscatter cross-section at two frequencies, 13.3 GHz and 400 MHz. It is shown that WKB method is applicable at both of these frequencies. Theoretical results are compared with the experimental results obtained from NASA Earth Resources Program mission 126. Theoretical results and experimental results are in good agreement.
Parashar, S. K.↗
Stability analysis of nonlinear autonomous systems - General theory and application to flutter
The analysis makes use of a singular perturbation method, the multiple time scaling. Concepts of stable and unstable limit cycles are introduced. The solution is obtained in the form of an asymptotic expansion. Numerical results are presented for the nonlinear flutter of panels and airfoils in supersonic flow. The approach used is an extension of a method for analyzing nonlinear panel flutter reported by Morino (1969).
Smith, L. L.↗
Effects of friction and heat conduction on sound propagation in ducts
A theoretical formulation of the propagation of sound in a viscous and heat conducting medium is presented. The problem is reduced to the determination of two scalar potentials related to pressure and entropy fluctuations respectively, and a vector potential related to vorticity fluctuations. The particular case of a two-dimensional duct of constant width is thoroughly investigated in the low, high, and very high frequency ranges. It is shown that three distinct families of modes may propagate along the duct axis, namely, pressure, entropy, and vorticity dominated modes. Perturbation methods are used to study the variations of attenuation rates, phase velocities, and mode shapes, as a function of frequency and duct width.
Huerre, P.↗