Edge-localized mode simulations in divertor tokamaks

The effect of wave propagation in nonhomogeneous elastic solid whose elastic parameters depend on one space coordinate only is considered. The stress and displacement components are assumed to depend on this same space coordinate and time alone. Taking Young’s modulus E=E0 cos αx and density ρ=ρ0 cos αx, we obtain the general solution for the problem of wave propagation in nonhomogeneous elastic rod. Particular cases in which a modified sawtooth, square, and half sine wave rectifier output as input wave, fed through one end of the rod, are studied, and the displacement u(x,t) is obtained. Graphs are drawn to study the behaviour of the input waves at time t=2 s, α=0.01, and =3.5.

H/D-isotope effects in chemical wave propagation on surfaces: the O 2+H 2 and NO+H 2 reactions on Rh(110) and Rh(111)

The effect of stress wave propagation on dynamic response of square tube was investigated by the experimental and numerical simulation methods in the present paper. The square tubes were subjected to the axial impact by split Hopkinson pressure bar. And the deformation process of each square tube was recorded by a high speed camera. Typical dynamic plastic buckling phenomena were observed in the experiments. And the numerical calculation of the experimental load case was conducted to analyze the effect of the stress wave propagation on the initial buckling of the square tube. The results show that there is obvious stress wave propagation in the square tube before the buckling of the square tube. And the initial buckling starts from the rear end of the tube due to the propagation of the stress wave. The relation between the stress wave propagation and initial buckling of the square tube was also discussed.

Recent efforts have extended fluid dynamic modeling to include low-electrical-conductivity (wavelike) electromagnetic field effects in plasmas. Here, we present results of a new study to explore and illustrate the capability of resolving such effects in the development of plasma instabilities. Recent work[1, 2] has explored the development of an efficient numerical procedure for simulating the coupled fluid dynamic and full electromagnetic (Maxwell) equations. This system of equations is more general than the resistive magnetohydrodynamic (MHD) model. The physical advantage to this system is that the inclusion of the displacement current and charge separation effects extends fluid dynamic modeling of plasmas to include regions of extremely low (or zero) electrical conductivity, where the electromagnetic fields possess a wave nature. Capturing the correct physical behavior of plasma instabilities in the limit of extremely low electrical conductivity is of significance for modern aerospace applications, including energy bypass arrangements for scramjet propulsion using magnetohydrodynamic augmentation, due to the extremely low electrical conductivity of the aerospace environment. The results depicted in this paper illustrate the potential for the numerical method realized in Ref. 1 to effectively resolve this behavior in cases where the MHD approximation may not be valid due to an exceedingly low electrical conductivity. A new study was initiated to explore more fully the capabilities to resolve regions of both low and high electrical conductivity using this numerical scheme. The problem selected for this study was the classic MHD KelvinHelmholtz instability. The initial and boundary conditions are provided in Ref. 2. A periodic box is initialized with two fluids of different density moving in opposite directions. An initial small perturbation is applied to the interfaces between the fluids, seeding an instability. A 256x256 grid size using a Roe solver for the coupled system of Navier-Stokes and full Maxwell equations was used, as detailed in [1, 2]. Three cases were explored: Case A was assigned a zero electrical conductivity, σ = 0 (purely hydrodynamic), Case B was given a small electrical conductivity of σ = 1, and Case C was given a very high conductivity of σ = 10 6 . Case A provides a hydrodynamic benchmark. Case B permits an investigation of a simulation that includes the effects of electromagnetic wave propagation in the plasma evolution. Case C effectively realizes the magnetohydrodynamic approximation. Results for the simulations are presented in a unique fashion in Fig. 1. For each subfigure, three spacetime isosurfaces of the density (blue, green and orange corresponding to the color range) have been depicted. Isosurfaces are the same for all three presented subfigures. Time flows from right (initial conditions) to left (final solution). For Case A, the fluid achieves a highly chaotic solution. The propagation of the initial disturbance at the interfaces between the two fluids is clear, as well as their development into a highly turbulent flow. Case B possesses an extremely low electrical conductivity, and therefore is not subject to the magnetic diffusion approximation of MHD. In fact, electromagnetic wave propagation was visible in this solution. The presence of a finite electrical conductivity provides some diffusion, but it does not match very well to the MHD prediction. However, the conductivity is large enough to abate the low-wavelength instabilities somewhat, and provide stability to the flow. Case C realizes the magnetohydrodynamic limit, where the magnetic field tends to stabilize the flow and strongly suppresses low-wavelength instabilities. A much more organized series of flow structures evolve through time to the final state. The magnetic field is effectively “frozen” to the fluid with such a large electrical conductivity, and the field strongly diffuses with little wave propagation.

Underwater sound propagation in areas of the continental shelf, shelf break, and continental slope can encounter strong horizontal reflection, refraction, diffraction, focusing, and/or defocusing due to a variety of environmental factors, including bathymetric variability, water column fluctuations (internal waves and shelf-break fronts), and boundary roughness. Theoretical, numerical, and experimental approaches have been taken to investigate the underlying physics of these three-dimensional (3-D) sound propagation effects and their temporal and spatial variability induced jointly by marine geological features and dynamic oceanographic processes. Some recent work on theoretical analysis, numerical modeling and field work experiments to study 3-D sound propagation in nonlinear internal wave ducts, over the continental slope and in submarine canyons will be reviewed in this talk. The ultimate goal of investing these 3-D sound propagation effects is to improve long-distance acoustical oceanographic technology in complex ocean environments. An example using a 3-D back-propagation method for acoustic inverse problems will be presented, along with discussion on feature applications. [Work supported by the Office of Naval Research.]

This paper presents a method for estimating the drag error in two-dimensional computational fluid dynamics simulations using a method that does not require auxiliary adjoint solutions. The error of interest is that caused by the numerical discretization, including effects of finite mesh size and approximation order. The target output is a drag calculation based on a farfield integration of the entropy. The error estimate is motivated by an interpretation of entropy variables as adjoint solutions to an entropy balance output. As entropy variables are obtained by a direct transformation of the state, no separate adjoint solution is required. The method is shown to be applicable not only to inviscid and laminar flows, but also to turbulent Reynolds-averaged Navier-Stokes flows, for which entropy variables generally lose their symmetrization property. Since the proposed drag error estimate is based on an integral of a weighted residual over the computational domain, it can be localized to provide an adaptive indicator over each element. Adaptive results for several flows of aerodynamic interest show that the error estimate is effective and that the method performs on par with adjoint-based methods. ∗Assistant Professor, AIAA Senior Member †Graduate Research Assistant ‡Professor, AIAA Fellow

Surface wave propagation effects on buried segmented pipelines

Wavefront shaping techniques allow one to focus light inside and through turbid media. In order to gain a better understanding how light evolves inside a scattering random medium while shaping the incident wavefront, it is beneficial to know the electromagnetic field within the entire medium, which is difficult to achieve in experiments. Here we investigate wavefront shaping techniques with numerical simulations based on Maxwell’s equations to examine various effects of wave propagation in randomly scattering media. First, we calculate numerically monochromatic plane wave solutions for a given scattering medium for different incident k-vectors. With these plane wave solutions we are able to simulate complex-shaped incident wavefronts impinging on the scattering medium. This enables us to scan and tilt the incident complex wavefront after solving Maxwell’s equations and to examine the electromagnetic field inside the medium. Due to the fact that we have access to the electromagnetic field of the plane wave illumination from different angles, it is easy to phase-optimize an incident wavefront by conjugating the known phase at a certain location. Because of the separate calculation of the plane wave solutions and the possibility to simulate different incident wavefronts by superimposing these plane wave solutions, our method is very dynamic and versatile. In summary, our simulation approach contributes to the understanding of light propagation in strongly scattering media such as biological tissue and to the improvement of medical imaging techniques.

Non-hydrostatic modeling of drag, inertia and porous effects in wave propagation over dense vegetation fields

A simple procedure, based on Love’s approximate theory [The Mathematical Theory of Elasticity (Cambridge U. P., Cambridge, England, 1927), 4th ed.] for wave propagation in a bar, is proposed in order to consider dispersive effects in wave propagation in a thin-walled, fluid-filled, elastomer tube. It is assumed that the perturbation from steady flow in the tube is small enough that a linearized theory is valid, and that the elastic modulus of the tube is small compared with the bulk modulus of the fluid so that compressibility of the fluid can be neglected. The flexural rigidity of the tube wall, the inertia of the tube wall, and the radial inertia of the fluid are taken into account, and an approximate expression for the dispersion relation for the fundamental mode is obtained. In order to investigate the dispersive effects, resulting from inclusion of the inertia and flexural rigidity of the tube wall and the radial inertia of the fluid in the model, an initial value problem is considered in detail. The fast Fourier transform is used to obtain numerical solutions for small and intermediate times. Numerical results are presented in graphical form.

Nonlinear saturation amplitudes (NSAs) of the first two harmonics in classical Rayleigh-Taylor instability (RTI) in cylindrical geometry for arbitrary Atwood numbers have been analytically investigated considering nonlinear corrections up to the fourth-order. The NSA of the fundamental mode is defined as the linear (purely exponential) growth amplitude of the fundamental mode at the saturation time when the growth of the fundamental mode (first harmonic) is reduced by 10% in comparison to its corresponding linear growth, and the NSA of the second harmonic can be obtained in the same way. The analytic results indicate that the effects of the initial radius of the interface (r0) and the Atwood number (A) play an important role in the NSAs of the first two harmonics in cylindrical RTI. On the one hand, the NSA of the fundamental mode first increases slightly and then decreases quickly with increasing A. For given A, the smaller the r0/λ (with λ perturbation wavelength) is, the larger the NSA of the fundamental mode is. When r0/λ is large enough (r0≫λ), the NSA of the fundamental mode is reduced to the prediction of previous literatures within the framework of third-order perturbation theory [J. W. Jacobs and I. Catton, J. Fluid Mech. 187, 329 (1988); S. W. Haan, Phys. Fluids B 3, 2349 (1991)]. On the other hand, the NSA of the second harmonic first decreases quickly with increasing A, reaching a minimum, and then increases slowly. Furthermore, the r0 can reduce the NSA of the second harmonic for arbitrary A at r0≲2λ while increase it for A ≲ 0.6 at r0≳2λ. Thus, it should be included in applications where the NSA has a role, such as inertial confinement fusion ignition target design.

Approximate analytical solution of the matrix transport equation for the mutual coherence function (MCF) of an acoustic field in terms of normal modes was derived. The proposed approach is capable of including stochastically rough surface as well as volume fluctuations in the index of refraction, and allowed one to reduce the problem of the MCF calculation in a refractive channel to the analogous problem in a free space. These results have been then employed to simulate the statistical effects of long-range sound propagation in realistic deep-water environments from the North-West Pacific on the horizontal array detection performance for several beamforming techniques. The most attention was paid to the gain degradation for the sound frequency of 250 Hz over megameter ranges under the basic assumption that internal waves or surface wind waves are, respectively, the main source of acoustic signal fluctuations. Rough surface scattering has been shown to cause the most significant effects. In particular, for the array length of order 100 acoustic wavelengths and wind speed of 15 m/s the coherence loss was of about 6 dB even for optimal quadratic processor and, in comparison, of about 12 dB for conventional plane-wave beamformer. [Work supported by Russian Basic Research Foundation, Grant No. 94-02-04544a.]

We are interested in identifying the mean-flow correction in the development of an instability. In the presented configuration (a 2D jet confined in a rectangular cavity that presents an oscillating instability), numerical simulations allow the identification of this mean-flow correction. We show that this distortion contributes to the non-linear saturation of the instability and that it is itself generated by the instability development: the action of the Reynolds tensor due to oscillating terms produces the mean-flow change.

In the summer of 2000, Duke University and the Kenyan power generation company, KenGen, conducted a microearthquake monitoring experiment at Longonot volcano in Kenya. Longonot is one of several major late Quaternary trachyte volcanoes in the Kenya Rift. They study was aimed at developing seismic methods for locating buried hydrothermal areas in the Rift on the basis of their microearthquake activity and wave propagation effects. A comparison of microearthquake records from 4.5 Hz, 2 Hz, and broadband seismometers revealed strong high-frequency site and wave-propagation effects. The lower frequency seismometers were needed to detect and record individual phases. Two-dozen 3-component 2- Hz L22 seismographs and PASSCAL loggers were then distributed around Longonot. Recordings from this network located one seismically active area on Longonot's southwest flank. The events from this area were emergent, shallow (<3 km), small (M<1), and spatially restricted. Evidently, the hydrothermal system in this area is not currently very extensive or active. To establish the nature of the site effects, the data were analyzed using three spectral techniques that reduce source effects. The data were also compared to a simple forward model. The results show that, in certain frequency ranges, the technique of dividing the horizontal motion by the vertical motion (H/V) to remove the source fails because of non-uniform vertical amplification. Outside these frequencies, the three methods resolve the same, dominant, harmonic frequencies at a given site. In a few cases, the spectra can be fit with forward models containing low velocity surface layers. The analysis suggests that the emergent, low frequency character of the microearthquake signals is due to attenuation and scattering in the near surface ash deposits.

The evolution of the ablative Rayleigh-Taylor instability in the presence of preheating of the cold pristine plasma ahead of the ablative front is investigated by two-dimensional numerical simulation. When the dependence of the linear ARTI growth rate on the excitation wavelength has a sharp maximum, a secondary spike-bubble structure at a harmonic of the excitation wavelength will be generated, leading to rupture of the original mode. On the other hand, for stronger preheating the linear growth rate has no sharp maximum and in the nonlinear evolution no competing secondary spike-bubble structure is generated. Instead, the original excitation evolves into an elongated jet. These results are in agreement with that from an analytical single-mode theory.