Plasmas involving strong electron drift in crossed electric and magnetic fields are of great interest for a number of applications such as space propulsion and material processing plasma sources. Specific applications include Hall thrusters, which are high efficiency, low thrust propulsion systems used on many missions for satellite orbit corrections and for future planned interplanetary missions, as well as magnetrons of various configurations used in plasma deposition devices. Similar conditions also exist in the E-layer of the ionosphere and on the Sun. Despite many successful applications of Hall thrusters and other Hall plasma sources, some aspects of their operation are still poorly understood. A particularly important problem is the anomalous electron transport, which greatly exceeds classical collisional values. Hall plasma devices exhibit numerous turbulent fluctuations in a wide frequency range and it is believed that fluctuations resulting from plasma instabilities are likely one of the main causes of the observed anomalous transport. Plasma turbulence also affects many other important processes such as electron injection, location of the ionization region and wall erosion among others that influence the operation and efficiency of Hall thrusters. In Hall thrusters, the E0xB0 flow is made unstable due to gradients in the plasma density, temperature and magnetic field. The gradient drift instabilities are long wavelength instabilities that propagate in the azimuthal direction. A fluid theory of these unstable modes is proposed. It is shown that a full account of the compressibility of the electron flow in inhomogeneous magnetic field leads to quantitative modifications of the previously obtained instability criteria and characteristics of the unstable modes. The ExB drift also drives ion sound type instabilities in Hall thrusters. The reactive/dissipative response of the closure current to the thruster walls drives these negative energy modes. A model for this type of instabilities is proposed and analyzed for typical Hall thruster conditions. It is shown how wall parameters modify the characteristic growth rate and frequency of the unstable modes and the related anomalous transport. Nonlinear phenomena are important to understand different aspects of the Hall thruster plasma dynamics. A nonlinear fluid model for the typical Hall thruster plasma is proposed. The model takes into account electron inertia, electron collisions with neutrals, density gradients as well as various nonlinear terms that arise from the electron drift and nonlinear polarization that were included via the gyroviscous cancellation. The proposed model includes the long wavelength and the low hybrid modes destabilized by density gradients and collisions. This system of fluid equations was implemented using the computational framework BOUT++ from which a set of nonlinear simulations of plasma turbulence was performed. It is shown from these first principles nonlinear simulations that small scale low hybrid oscillations result in an anomalous electron current significantly exceeding the classical collisional current.

This thesis focuses on investigating the stability, dynamics and physical mechanisms of thermocapillary flows undergoing phase change by means of direct numerical simulations and experiments. The novelty of the general approach developed in this work lies in the fact that the problems under consideration are addressed with novel fully-coupled transient two-phase flow models in 3D. Traditional simplifications are avoided by accounting for deformable interfaces and by addressing advection-diffusion mechanisms not only in the liquid but also in the gas. This strategy enables a realistic investigation of the interface energy and mass transfer at a local scale for the first time. Thorough validations of the models against theory and experiments are presented. The thesis encompasses three situations in detail: liquid layers in saturated environments, liquid layers in unsaturated environments and evaporation of liquid droplets. Firstly, a model grounded in the volume-of-fluid method is developed to study the stability of laterally-heated liquid layers under saturated environments. In this configuration, the planar layer is naturally vulnerable to the formation of an oscillatory regime characterized by a myriad of thermal wave-like patterns propagating along the gas-liquid interface, i.e. hydrothermal waves. The nonlinear growth of the instabilities is discussed extensively along with the final bulk flow for both the liquid and gas phases. Previously unknown interface deformations, i.e. physical waves, induced by, and enslaved to, the hydrothermal waves are reported. The mechanism of heat transfer across the interface is found to contradict previous single-phase studies since the travelling nature of the hydrothermal waves leads to maximum heat fluxes not at the points of extreme temperatures but somewhere in between. The model for saturated environments is extended in a second stage to assess the effect of phase change in the hydrothermal waves for the first time. New numerical results reveal that evaporation affects the thermocapillary instabilities in two ways: the latent energy required during the process tends to inhibit the hydrothermal waves while the accompanying level reduction enhances the physical waves by minimizing the role of gravity. Interestingly, the hydrothermal-wave-induced convective patterns in the gas decouple the interface vapour concentration with that in the bulk of the gas leading to the formation of high (low) concentrations of vapour at a certain distance above interface cold (hot) spots. At the interface the behavior is the opposite. The phase-change mechanism for stable layers is also discussed. The Marangoni effect plays a major role in the vapour distribution and local evaporation flux and can lead to the inversion of phase-change process, i.e. the thermocapillary flow can result into local condensation in an otherwise evaporating liquid layer. The third problem discussed in this thesis concerns with the analysis of evaporating sessile droplets by means of both experiments and 3D numerical modeling. An experimental apparatus is designed to study the evaporation process of water droplets on superheated substrates in controlled nitrogen environments. The droplets are simultaneously recorded with a CCD camera from the side and with an infrared camera from top. It is found that the contact line initially remains pinned for at least 70% of the time, period after which its behaviour changes to that of the stick-slip mode and the drop dries undergoing contact line jumps. For lower temperatures an intermediate stage has been observed wherein the drop evaporates according to a combined mode. The experimental work is complemented with numerical simulations. A new model implementing the diffuse-interface method has been developed to solve the more complex problems of this configuration, especially those associated with the intricate contact-line dynamics. Further insights into the two-phase flow dynamics have been provided as well as into the initial transient stage, in which the Marangoni effect has been found to play a major role in the droplet heating. For the first time, a fully-coupled two-phase direct numerical simulations of sessile drops with a moving contact line has been performed. The last part of this work has been devoted to the investigation of three-dimensional phenomena on drops with irregular contact area. Non-sphericity leads to complex three-dimensional drop shapes with intricate contract angle distributions along the triple line. The evaporation rate is found to be affected by 3D features as well as the bulk flow, which become completely non-axisymmetric. To the best of our knowledge, this work is the first time that three-dimensional two-phase direct numerical simulations of evaporating sessile drops have been undertaken.

The propagation and stability of waves in relativistic astrophysical plasmas is presented. Our investigation, using a relativistic two-fluid model, is different from previous relativistic fluid studies in that the plasma is treated fully relativistically, both in temperature and in directed speed. Much of this study is devoted to relativistic linear waves in pulsar pair plasmas, with a view to elucidating a possible mechanism for pulsar radio wave emission. We also study interesting nonlinear exact solutions in both relativistic and non-relativistic plasmas. Pulsar pair plasmas can support four transverse modes for parallel propagation. Two of these are electromagnetic plasma modes, which at high temperature become light waves. The remaining two are Alfvénic modes, split into a fast and a slow mode. The slow mode, always sub-luminous, is cyclotron (Alfvén) two-stream unstable at large wavelengths. We find that temperature effects, within the fluid model used, do not suppress the instability in the limit of large (finite) magnetic field. The fast Alfvén mode can be super-luminous only at large wavelengths; however, it is always sub-luminous at high temperatures. In this incompressible approximation, only the ordinary mode is present for perpendicular propagation. We discuss the implications of the unstable mode for radio emission mechanisms. For typical values, the instability is quite fast, and the waves can grow to sizable levels, such that, the magnetic modulation could act as a wiggler. The pulsar primary beam interacting with this wiggler, could drive a free electron laser (FEL) effect, yielding coherent radiation. Investigation of the FEL in this setting and demonstrating that the frequency spectral range, and luminosities, predicted by this mechanism is well within the observed range of radio frequency (and luminosity) emissions, is one of the principal results of this dissertation. It is tempting to speculate, then, that an FEL-like radiation effect could be responsible for the highly coherent radio wave emissions from pulsars. In the study of nonlinear exact solutions we have generalized the results to the incompressible Hall Magnetohydrodynamics (HMHD). We find that for cases when the plasma is weakly magnetized the frequencies of the modes decrease as the wave amplitude (effective mass) increases. For very strongly magnetized plasmas the light-like modes tend to be asymptotically linear; the frequency is unaffected by wave amplitude. / text

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Approved for public release; distribution is unlimited / The time varying development and structure of Dean vortices were studies using flow visualization. Observations were made over a range of Dean numbers from 40 to 200 using a transparent channel with mild curvature, 40:1 aspect ratio, and an inner to outer radius ratio of 0.979. Seven flow visualization techniques were tried but only one, a wood burning smoke generator, produced usable results. Different vortex characteristics were observed and documented in sequences of photographs space one quarter of a second apart at locations ranging from 85 to 135 degrees from the start of curvature. Evidence is presented that supports the twisting/rocking nature of the flow. / http://archive.org/details/flowvisualizatio00bell / Lieutenant, United States Navy

We study the formation of planetesimals in protoplanetary disks from the gravitational collapse of solid over-densities generated via the streaming instability. To carry out these studies, we implement and test a particle-mesh self-gravity module for the ATHENA code that enables the simulation of aerodynamically coupled systems of gas and collisionless self-gravitating solid particles. Upon employment of our algorithm to planetesimal formation simulations, we find that (when a direct comparison is possible) the ATHENA simulations yield predicted planetesimal properties that agree well with those found in prior work using different numerical techniques. In particular, the gravitational collapse of streaming-initiated clumps leads to an initial planetesimal mass function that is well-represented by a power law, dN / dM(p) proportional to M-p(-p), with p similar or equal to 1.6 +/- 0.1, which equates to a differential size distribution of dN / dR(p) proportional to R-p(-q), with q similar or equal to 2.8 +/- 0.1. We find no significant trends with resolution from a convergence study of up to 512(3) grid zones and N-par approximate to 1.5 x 10(8) particles. Likewise, the power-law slope appears indifferent to changes in the relative strength of self-gravity and tidal shear, and to the time when (for reasons of numerical economy) self-gravity is turned on, though the strength of these claims is limited by small number statistics. For a typically assumed radial distribution of minimum mass solar nebula solids (assumed here to have dimensionless stopping time tau = 0.3), our results support the hypothesis that bodies on the scale of large asteroids or Kuiper Belt Objects could have formed as the high-mass tail of a primordial planetesimal population.

In the deformation of layered materials such as geological strata, or stacks of paper, mechanical properties compete with the geometry of layering. Smooth, rounded corners lead to voids between layers, while close packing leads to geometrically induced curvature singularities. When creation of voids is penalized by external pressure, the system trades off these competing effects, leading to various accommodating formations. Three two dimensional energy based nonlinear models are presented to describe the formation of voids at areas of intense geological folding. For each model the layers are assumed to be flexible elastic beams under hard unilateral contact constraint; which are solved as quasi-static obstacle problems with a free boundary. In each case an application of Kuhn-Tucker theory leads to representation as a nonlinear fourth order differential equation. Firstly a single layered model for voiding is presented. An elastic layer is forced into a V-shaped singularity by a uniform overburden pressure, where the fourth order free boundary problem is shown to have a unique, convex, symmetric solution. Drawing parallels with the Kuhn-Tucker theory, virtual work and ideas of duality, the physical significance of this differential equation is emphasised. Finally, appropriate scaling of either the potential energy or the differential equation shows the solutions scale to a single parametric group, for which the size of the void scales inversely with the ratio of overburden pressure to bending stiffness of the layer. Common to structural geology, one or several especially thick layers can dominate the deformation process. As a result, the remaining weak layers must accommodate into the geometry imposed by these competent layers. The second model, extends the first by introducing a plastic hinge to replicate the geometry imposed by the competent layer, and also axial springs to resist the slip over the limbs. The equilibrium equations for the system are investigated using the mathematical techniques developed for the first model. Under rigid loading the system may snap from an initially flat state to a convex voiding solution, as seen in the first model. However, if resistance to slip is high, the slightest imperfection causes the system to jump to a convoluted up-buckled solution, following a de-stiffened path to a point of self contact. These solutions have similarities with the delamination of carbon fibre composites. Finally, we extend the two single layered models to a simple multilayered model, which describes the periodic formation of voids in a chevron fold. The model shows that in the limit of high overburden pressures solutions form voids every layer, producing straight limbs punctured by sharp corners. This analysis shows good agreement when compared with recent experiments. This work provides the basis for future work on the buckling of thin multilayer assemblies in which voids may develop, and emphasizes the importance of the intricate nonlinear constraints of layers fitting together in multilayered folds.

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