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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Static Whirling Rods: Past researchers suggested that “static instabilities” exist at certain rotational speeds of whirling rods. This thesis shows these instabilities are an artefact of the material constitutive laws that are being used well outside their range of applicability. An alternative approach is developed where strains due to rotation are separated from the superimposed vibration. This enables the generally predicted lowering of longitudinal natural frequencies with rotational speed shown to be simply a result of the bulk changes in the geometry of whirling rods. Steady state equations of whirling rods are formulated in Lagrangian coordinates. Due to the non-linear nature of the governing equations, an original numerical method is applied to solve the problem. Numerical results are compared with analytical results obtained from the linearized uniaxial model. There is a close agreement between these two models at low angular velocities. However, at high angular velocities, discrepancies between them arise, confirming that the nonlinear strain-displacement relationship has significant effect on the results and the inferred “static instabilities”. This approach first solves the “static” problem of the deformed geometry of a highly strained whirling rod before longitudinal natural modes are determined by classical methods. Furthermore, conditions for existence and uniqueness of solutions are derived. Dynamic Rotating Annuli: In-plane modes of vibration of annular plates are investigated. Two different models of equations one from Bhuta and Jones and the other from Biezeno and Grammel that govern the rotational motions of annuli will be studied. Since Biezeno and Grammel’s model was originally derived in Eulrian coordinates, their model will be transformed to the Lagrangian coordinates for the purpose of comparison with Bhuta and Jones’ model. / The solutions of the equations assume small oscillations of vibration being superimposed on the steady state of the annulus while it is in rotation. Exact and approximate solutions are obtained for the Bhuta and Jones’ model, where the approximate solutions on in-plane displacements and natural frequencies are acquired by ignoring the Coriolis effect. A proposed numerical scheme is implemented to solve the governing equations coupled with radial and circumferential displacements. Uniqueness of solutions will be mentioned although it will not be rigorously derived because it is out of the scope of this thesis. Approximate analytical results show that both radial and circumferential natural frequencies are decreasing when the rotational speed of an annulus is increasing. The exact and numerical results on both models that take the Coriolis effect into account show that radial natural frequencies are increasing and circumferential natural frequencies are decreasing when the rotational speed of an annulus is increasing.