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NASA NTRS1986

Nongeostrophic theory of zonally averaged circulation. I - Formulation

A nongeostrophic theory of zonally averaged circulation is formulated using the nonlinear primitive equations (mass conservation, thermodynamics, and zonal momentum) on a sphere. The relationship between the mean meridional circulation and diabatic heating rate is studied. Differences between results of nongeostropic theory and the geostrophic formulation concerning the role of eddy forcing of the diabatic circulation and the nonlinear nearly inviscid limit versus the geostrophic limit are discussed. Consideration is given to the Eliassen-Palm flux divergence, the Eliassen-Palm pseudodivergence, the nonacceleration theorem, and the nonlinear nongeostrophic Taylor relationship.

Tung, Ka Kit↗

NASA NTRS1987

Ginzburg-Landau theory for the solid-liquid interface of bcc elements

Consideration is given to a simple order-parameter theory for the interfacial tension of body-centered-cubic solids in which the principal order parameter is the amplitude of the density wave at the smallest nonzero reciprocal-lattice vector of the solid. The parameters included in the theory are fitted to the measured heat of fusion, melting temperature, and solid-liquid density difference, and to the liquid structure factor and its temperature derivative at freezing. Good agreement is found with experiment for Na and Fe and the calculated anisotropy of the surface tension among different crystal faces is of the order of 2 percent. On the basis of various assumptions about the universal behavior of bcc crystals at melting, the formalism predicts that the surface tension is proportional to the heat of fusion per surface atom.

Shih, W. H.↗

NASA NTRS1987

Composite box beam analysis - Theory and experiments

Beam theory is widely used as a first approximation in numerous structural applications. When applied to composite beams, the accuracy of beam theory becomes questionable because (1) the shearing and warping deformations become significant, as the shearing stiffness of composite laminates is often very low, and (2) several elastic couplings can occur that strongly influence the behavior of composite beams. The torsional behavior of thin-walled composite beams has important implications for aeronautical structures and is deeply modified by the above nonclassical effects. This paper presents two comprehensive analysis methodologies for composite beams and describes experimental results obtained from a thin-walled, rectangular cross-sectional beam. The theoretical predictions are found in good agreement with the observed twist and strain distributions. Out-of-plane torsional warping of the cross-section is found to be the key factor for an accurate modeling of the torsional behavior of such structures.

Bauchau, O. A.↗

NASA NTRS1986

Consistency relations for spinning matter in gravitational theories

The consistency equations for a charged spinning fluid in the Einstein-Cartan theory are examined. The hydrodynamic laws associated with the theory of Ray and Smalley (1982, 1983) and the electromagnetic extension of Amorim (1984, 1985) are studied. The derivation of the consistency equation from the Euler equations for an improved perfect-fluid energy-momentum tensor is described.

Ray, John R.↗

NASA NTRS1987

On the development of the theory of the QBO

The events that led to the discovery of the quasi-biennial oscillation (QBO) of the equatorial stratosphere are described together with the development of current QBO theory. Three independent areas of inquiry led to this theory: (1) the observational and theoretical studies of equatorial waves, (2) the theoretical study of the behavior of mountain waves at critical levels where the mean flow speed went to zero, and (3) the semiempirical study of the momentum budget of the QBO. The efforts in each of these three areas are discussed.

Lindzen, Richard S.↗

NASA NTRS1987

Origin of low-frequency (intraseasonal) oscillations in the tropical atmosphere. I - Basic theory

A theory for the origin of intraseasonal oscillations of the tropical atmosphere is presented. The theoretical background for and main features of the intraseasonal variability of the tropical atmosphere are discussed. The theory is validated for the 40-50 day oscillation using a simple model. The transient response of the tropical atmosphere to a local oscillating heat source and an internally forced heat source is studied. The structure and mechanism of the eastward propagation are examined. It is noted that the eastward propagation of low-frequency oscillation is the result of the interaction between convection and dynamics via the mobile wave-CISK mechanism. It is suggested that the low-frequency oscillations are an intrinisic atmospheric phenomena that exist without a dynamically interactive ocean.

Lau, K.-M.↗

NASA NTRS1987

Imaging radar polarization signatures - Theory and observation

Radar polarimetry theory is reviewed, and comparison between theory and experimental results obtained with an imaging radar polarimeter employing two orthogonally polarized antennas is made. Knowledge of the scattering matrix permits calculation of the scattering cross section of a scatterer for any transmit and receive polarization combination, and a new way of displaying the resulting scattering cross section as a function of polarization is introduced. Examples of polarization signatures are presented for several theoretical models of surface scattering, and these signatures are compared with experimentally measured polarization signatures. The coefficient of variation, derived from the polarization signature, may provide information regarding the amount of variation in scattering properties for a given area.

Van Zyl, Jakob J.↗

NASA NTRS1985

Finite-time arbitrary-motion unsteady cascade airfoil theory for helicopter rotors in hover

A complete and detailed derivation of finite-time arbitrary-motion cascade theory is presented for both Laplace and frequency domains. This theory includes the effect of returning wakes for both single- and multibladed rotors. The generalized cascade lift-deficiency function (CLDF) is shown to be consistent with the generalized Theodorsen lift-deficiency function when the wake spacing approaches infinity or when the reduced frequency tends to infinity. This function predicts correct zero-reduced-frequency limit. Accurate and efficient numerical procedures are presented for the evaluation of the CLDF. Numerical examples comparing the CLDF with Loewy's lift deficiency function in frequency domain are presented. Accurate Pade approximants of the CLDF are constructed using a Bode-plot approach which allows for complex poles.

Dinyavari, M. A. H.↗

NASA NTRS1986

Experimental verification of corrosive vapor deposition rate theory in high velocity burner rigs

The ability to predict deposition rates is required to facilitate modelling of high temperature corrosion by fused salt condensates in turbine engines. A corrosive salt vapor deposition theory based on multicomponent chemically frozen boundary layers (CFBL) has been successfully verified by high velocity burner rig experiments. The experiments involved internally air-impingement cooled, both rotating full and stationary segmented cylindrical collectors located in the crossflow of sodium-seeded combustion gases. Excellent agreement is found between the CFBL theory and the experimental measurements for both the absolute amounts of Na2SO4 deposition rates and the behavior of deposition rate with respect to collector temperature, mass flowrate (velocity) and Na concentration.

Gokoglu, Suleyman A.↗

NASA NTRS1987

A general theory for dynamic instability of tube arrays in crossflow

A general theory of fluidelastic instability for a tube array in crossflow is presented. Various techniques to obtain the motion-dependent fluid-force coefficients are discussed and the general instability characteristics are summarized. The theory is also used to evaluate the results of other mathematical models for crossflow-induced instability.

Chen, S. S.↗

NASA NTRS1988

Effective-Mass Theory For Inhomogeneous Semiconductors

Five papers present derivations in effective-mass theory for semiconducing materials of gradually varying spatial composition. In paper entitled "Position-Dependent Effective Masses in Semiconductor Theory," concept of spatially-varying effective masses reviewed and shown unworkable. Second paper considers compound semiconductor having gradual spatial variation of composition. Third paper shows effective masses depend on average of chemical composition over entire crystal. Pair of papers entitled "Forces Acting on Free Carriers in Semiconductors of Inhomogeneous Composition" show it is incorrect to apply extended Wannier-Slater theorem using spatially changing effective masses, and quasi-electric fields due to spatial variations in chemical composition do not depend explicitly on temperature.

Von Roos, Oldwig↗

NASA NTRS1986

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.↗

NASA NTRS1988

A theory of viscoplasticity accounting for internal damage

A constitutive theory for use in structural and durability analyses of high temperature isotropic alloys is presented. Constitutive equations based upon a potential function are determined from conditions of stability and physical considerations. The theory is self-consistent; terms are not added in an ad hoc manner. It extends a proven viscoplastic model by introducing the Kachanov-Rabotnov concept of net stress. Material degradation and inelastic deformation are unified; they evolve simultaneously and interactively. Both isotropic hardening and material degradation evolve with dissipated work which is the sum of inelastic work and internal work. Internal work is a continuum measure of the stored free energy resulting from inelastic deformation.

Freed, A. D.↗

NASA NTRS1988

Cyclic uniaxial and biaxial hardening of type 304 stainless steel modeled by the viscoplasticity theory based on overstress

The isotropic theory of viscoplasticity based on overstress does not use a yield surface or a loading and unloading criterion. The inelastic strain rate depends on overstress, the difference between the stress and the equilibrium stress, and is assumed to be rate dependent. Special attention is paid to the modeling of elastic regions. For the modeling of cyclic hardening, such as observed in annealed Type 304 stainless steel, and additional growth law for a scalar quantity which represents the rate independent asymptotic value of the equilibrium stress is added. It is made to increase with inelastic deformation using a new scalar measure which differentiates between nonproportional and proportional loading. The theory is applied to correlate uniaxial data under two step amplitude loading including the effect of further hardening at the high amplitude and proportional and nonproportional cyclic loadings. Results are compared with corresponding experiments.

Yao, David↗

NASA NTRS1987

Evaluation of a theory for pressure-strain rate

A theoretical expression for the slow part (the nonlinear fluctuation part) of the pressure-strain rate is compared with simulations of anisotropic homogeneous flows. The objective is to determine the quantitative accuracy of the theory and to test its prediction that the generalized Rotta coefficient, a non-dimensionalized ratio of slow term to the Reynolds stress anisotropy, varies with direction and can be negative. Comparisons are made between theoretical and simulation values of the slow term itself and of the generalized Rotta coefficients. The implications of the comparison for two-point closure theories and for Reynolds stress modeling are pointed out.

Weinstock, J.↗

NASA NTRS1988

Processing deficits in monitoring analog and digital displays: Implications for attentional theory and mental-state estimation research

Subjects performed short term memory tasks, involving both spatial and verbal components, and a visual monitoring task involving either analog or digital display formats. These two tasks (memory vs. monitoring) were performed both singly and in conjunction. Contrary to expectations derived from multiple resource theories of attentional processes, there was no evidence that when the two tasks involved the same cognitive codes (i.e., either both spatial or both verbal/linguistics) there was more of a dual task performance decrement than when the two tasks employed different cognitive codes/processes. These results are discussed in terms of their implications for theories of attentional processes and also for research in mental state estimation.

Payne, David G.↗

NASA NTRS1988

Saturation and the limit of jet mixing enhancement by single frequency plane wave excitation: Experiment and theory

The limitations of single frequency plane wave excitation in mixing enhancement are investigated for a circular jet. Measurements made in an 8.8 cm diameter jet are compared with a theoretical model. The measurements are made to quantify mixing at excitation amplitudes up to 2 percent of the jet exit velocity. The initial boundary layer state, the exit mean and fluctuating velocity profiles and spectra are documented for all cases considered. The amplitude of the fundamental wave is recorded along the jet axis for various levels of excitation. As the amplitude of excitation is increased the jet spreading rate is increased, but beyond a saturation amplitude further increases have no effect on the spreading. The experimental results are compared with theoretical estimates. In the theory the flow is split into the mean flow, large scale motions, and fine scale turbulence. Shape assumptions for the mean flow, and fine scale turbulence along with the shape for the large scale motions obtained from a linear stability theory provide the closure. The experimental results compare reasonably well with predictions.

Raman, Ganesh↗

NASA NTRS1987

Complex space multipole theory for scattering and diffraction problems

Classical multipole theory can be extended to multipoles located in complex space and applied in scattering and diffraction problems with the advantage that, if the point of the multipole is correctly chosen, the first term may give an order of magnitude better approximation to the source than when the multipole is in real space. The basic theory, given elsewhere, is presented here in a more straightforward manner and the improvement in radiation pattern is demonstrated for sources of constant polarization. Applications on scattering by spheroidal dielectric bodies and diffraction by a dielectric half-space are discussed.

Lindell, Ismo V.↗