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Iterative solution to Krook-Boltzmann kinetic equation noting Navier-Stokes numerical solution, computation and analysis of distribution function within shock wave
This paper presents some numerical experiments performed with the TFM to study the various wave components excited in the auroral regions that propagate through the thermosphere and lower atmosphere, and to demonstrate the properties of realistic source geometries. The model is applied to the interpretation of satellite measurements, and gravity waves seen in the thermosphere of Venus are discussed. Gravity waves are prominent in the terrestrial thermosphere polar region and can be excited by perturbations in Joule heating and Lorentz force due to magnetospheric processes. Observations from the Dynamics Explorer-2 satellite are used to illustrate the complexity of the phenomenon and to review the TFM that is utilized.
Feynman integral for classical waves evaluated, using Hamiltonian approach to summation
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A theoretical model for the interaction of a turbulent boundary layer with an oscillating wavy surface over which a fluid is flowing is developed, with an application to wind-driven water waves and to panel flutter in low supersonic flow. A systematic methodology is developed to obtain the surface pressure distribution by considering separately the effects on the perturbed flow of a mean shear velocity profile, viscous stresses, the turbulent Reynolds stresses, compressibility, and three-dimensionality. The inviscid theory is applied to the wind-water wave problem by specializing to traveling-wave disturbances, and the pressure magnitude and phase shift as a function of the wave phase speed are computed for a logarithmic mean velocity profile and compared with inviscid theory and experiment. The results agree with experimental evidence for the stabilization of the panel motion due to the influence of the unsteady boundary layer.
A model inverse design problem is used to investigate the effect of flow discontinuities on the optimization process. The optimization involves finding the cross-sectional area distribution of a duct that produces velocities that closely match a targeted velocity distribution. Quasi-one-dimensional flow theory is used, and the target is chosen to have a shock wave in its distribution. The objective function which quantifies the difference between the targeted and calculated velocity distributions may become non-smooth due to the interaction between the shock and the discretization of the flowfield. This paper offers two techniques to resolve the resulting problems for the optimization algorithms. The first, shock-fitting, involves careful integration of the objective function through the shock wave. The second, coordinate straining with shock penalty, uses a coordinate transformation to align the calculated shock with the target and then adds a penalty proportional to the square of the distance between the shocks. The techniques are tested using several popular sensitivity and optimization methods, including finite-differences, and direct and adjoint discrete sensitivity methods. Two optimization strategies, Gauss-Newton and sequential quadratic programming (SQP), are used to drive the objective function to a minimum.
Sensitive, high resolution plasma probes for analysis of the distribution functions and plasma wave instruments for measurements of electromagnetic and electrostatic wave modes are commonly flown together to provide information on plasma instabilities and wave particle interactions. Analysis of the data for the ISEE 3 mission is provided.
In this task, we focused on developing corrosion-resistant claddings for wave energy applications. Wave energy systems are exposed to saline conditions, which are corrosive to many metallic structural materials (e.g., carbon steel). Corrosion-resistant (stainless) steels are typically alloyed with >18% chromium (Cr) and >8% nickel (Ni), which dramatically raises material costs and can hinder the development of wave energy systems; thus, coatings are a necessary corrosion protection method for most. Non-metallic coatings (paint, epoxy) have shorter service lives, limited resistance to mechanical stress and wear, plus additional costs of inspection and eventual replacement. Therefore, overlay stainless steel (SS) claddings have a cost-effective use case for protecting components from corrosion, particularly for those that may be subject to mechanical stress / wear and with long service lives.
In a recent study of variational improvement of the Kirchhoff approximation for electromagnetic scattering by rough surfaces, a key ingredient in the variational principle was found to diverge for important configurations (e.g., backscatter) if the polarization had any vertical component. The cause and a cure of this divergence are discussed here. The divergence is demonstrated to occur for arbitrary perfectly conducting scatterers and its universal characterstics are determined, by means of a general divergence criterion that is derived. A variational cure for the divergence is prescribed, and it is tested successfully on a standard scattering model.
Emission of resonance fluorescence by an atom near the surface of a four-wave mixing phase conjugator is considered. The dipole radiation field, regarded as a Heisenberg-operator field, is decomposed into plane waves with the aid of Weyl's representation of the Green's function for the wave equation. Each plane-wave component which is incident on the surface of the nonlinear medium, is reflected as its phase-conjugate image. Summation of all reflected plane waves then yields the phase conjugate replica of the incident dipole radiation. This field adds to the radiation which is emitted by the atom into the direction away from the medium. The condition under which squeezing occurs in the emitted resonance fluorescence is investigated.
The Landsat Image Data Quality Analysis (LIDQA) Program conducted by NASA has the objective to quantify the performance of the Thematic Mapper (TM) on the Landsat-4 and Landsat-5 spacecraft. The interest in the spatial resolution performance of the TM is partly related to the decrease of the instantaneous field of view (IFOV) from 80 m for the MSS to 30 m for the TM. Studies related to the preflight line spread function (LSF), square wave response (SWR), and theoretical component modeling of the TM system modulation transfer function (MTF) have been conducted. However, the need remains to estimate the MTF of the complete system. The present paper is concerned with investigations related to this task. Attention is given to three approaches for measuring the MTF of the TM system from imagery.
The effect of wave breaking on the probability function of surface elevation is examined. The surface elevation limited by wave breaking zeta sub b(t) is first related to the original wave elevation zeta(t) and its second derivative. An approximate, second-order, nonlinear, non-Gaussian model for zeta(t) of arbitrary but moderate bandwidth is presented, and an expression for the probability density function zeta sub b(t) is derived. The results show clearly that the effect of wave breaking on the probability density function of surface elevation is to introduce a secondary hump on the positive side of the probability density function, a phenomenon also observed in wind wave tank experiments.
Calculation of e-H total and elastic partial wave cross sections is being carried out using the complex correlation variational T-matrix method. In this preliminary study, elastic partial wave phase shifts are calculated with the correlation functions which are confined to be real. In that case the method reduces to the conventional optical potential approach with projection operators. The number of terms in the Hylleraas-type wave function for the S phase shifts is 95 while for the S it is 56, except for k=0.8 where it is 84. Our results, which are rigorous lower bounds, are given. They are seen to be in general agreement with those of Schwartz, but they are of 0 greater accuracy and outside of his error limits for k=0.3 and 0.4 for S. The main aim of this approach' is the application to higher energy scattering. By virtue of the complex correlation functions, the T matrix is not unitary so that elastic and total scattering cross sections are independent of each other. Our results will be compared specifically with those of Bray and Stelbovics.
Calculation of e(-) - H total and elastic partial wave cross sections is being carried out using the complex correlation variational T-matrix method. In this preliminary study, elastic partial wave phase shifts are calculated with the correlation functions which are confined to be real. In that case the method reduces to the conventional optical potential approach with 2 projection operators. The number of terms in the Hylleraas-type wave function for the S-1 phase shifts is 95 while for the S-3 it is 56, except for k = 0.8 where it is 84. Our results, which are rigorous lower bounds, are seen to be in general agreement with those of Schwartz, but they are of greater accuracy and outside of his error limits for k = 0.3 and 0.4 for S-1. The main aim of this approach is the application to higher energy scattering. By virtue of the complex correlation functions, the T-matrix is not unitary so that elastic and total scattering cross sections are independent of each other. Our results will be compared specifically with those of Bray and Stelbovics.
Electric and magnetic field instruments on the DE 1 spacecraft provided observations of toroidal standing wave oscillations of magnetic shells in 1981 and 1982. The amplitude and nodal structure of these waves, as a function of increasing magnetic latitude, was studied and compared with model calculations of these waves. Eight pulsation events were selected for study. The pulsations in these events ranged in period from 20 to 300 s. They were observed at L values between 2.8 and 9.7 and at magnetic latitudes from the equator to 48 deg. The duration of these pulsation events was 20 to 30 min, and they usually consisted of a 5- to 10-min growth in amplitude, a 5- to 10-min interval of fluctuating amplitude, and a 5- to 20-min interval of decreasing amplitude. The relative E and B amplitudes and the phase relations between the E and B waves could be qualitatively explained by the nodal structure of the waves predicted by model calculations. Detailed quantitative comparisons of E and B amplitudes were in agreement with more recent model calculations. In a few cases, electron densities were also available as derived from plasma frequency observations; in these cases the standing wave periods calculated were reasonably close to, but somewhat less than, the observed periods.
On the basis of the mapping method developed by Huang et al. (1983), an analytic expression for the non-Gaussian joint probability density function of slope and elevation for nonlinear gravity waves is derived. Various conditional and marginal density functions are also obtained through the joint density function. The analytic results are compared with a series of carefully controlled laboratory observations, and good agreement is noted. Furthermore, the laboratory wind wave field observations indicate that the capillary or capillary-gravity waves may not be the dominant components in determining the total roughness of the wave field. Thus, the analytic results, though derived specifically for the gravity waves, may have more general applications.
A transfer function approach is taken in constructing a spectral model of the acoustic-gravity wave response in a multiconstituent thermosphere. The model is then applied to describing the thermospheric response to various sources around the globe. Zonal spherical harmonics serve to model the horizontal variations in propagating waves which, when integrated with respect to height, generate a transfer function for a vertical source distribution in the thermosphere. Four wave components are characterized as resonance phenomena and are associated with magnetic activity and ionospheric disturbances. The waves are either trapped or propagate, the latter becoming significant when possessing frequencies above 3 cycles/day. The energy input is distributed by thermospheric winds. The disturbances decay slowly, mainly due to heat conduction and diffusion. Gravity waves appear abruptly and are connected to a sudden switching on or off of a source. Turn off of a source coincides with a reversal of the local atmospheric circulation.
The present investigation has the objective to study the precipitation of energetic electrons into the ionosphere due to the interaction of these particles with short-duration VLF waves in the magnetosphere. The physics of the interaction is considered, taking into account the wave structure, the energetic particle distribution, wave-particle interaction, and the computation of the precipitated flux versus time. The obtained formulation is applied to various different magnetospheric conditions. Attention is also given to peak flux and total deposited energy. The results of the investigation demonstrate the role of the energetic particle distribution function, the normalized wave frequency, the L value of the path of propagation, the cold plasma density, and the wave intensity. The precipitated energy flux that would be observed at 1000-km altitude is presented as a function of time relative to the injection of the wave pulse at the same point.