The upstream propagating acoustic waves and Kelvin-Helmholtz instability waves associated with supersonic twin jets are investigated using a vortex sheet mode. For the instability waves, a second model which takes into account the finite thickness of the jet mixing layer is also used. For each jet model, dispersion relations of the instability and acoustic saves are derived. The eigenvalues and eigenfunctions are classified into four linearly independent families according to the symmetry of eigenfunctions. Within each family there are an infinite number of modes. / A parametric study of the acoustic and instability wave eigenvalues and eigenfunctions has been carried out. Numerical results of the total growths show that the most unstable wave mode for each family is the flapping mode. Under a given operating condition, the flapping modes of family 1 and family 2 are the most dominant. It is found that the wave frequencies of the upstream propagating acoustic waves are confined to narrow bands. Formulas of cutoff points of dispersion curves of upstream propagating acoustic waves are derived. These formulas can be used to provide a first estimate of the screech tones frequencies of twin supersonic jets. / Source: Dissertation Abstracts International, Volume: 54-11, Section: B, page: 5755. / Major Professor: Christopher K. W. Tam. / Thesis (Ph.D.)--The Florida State University, 1993.

A method for calculating the acoustic radiation generated by the large scale instabilities of axisymmetric jets is developed. The characteristics of the flow instabilities are obtained from the linearized, inviscid, compressible equations of motion in terms of an asymptotic expansion. This asymptotic expansion is not uniformly valid far away from the jet flow. To obtain a solution valid far away from the jet, the method of matched asymptotic expansions is used. The matching of inner and outer solutions provide two very important results. First, a new interpretation of the eigenvalue problem of classical instability theory is given. Secondly, matching provides a method for determining the slow varying wave amplitude of the instability wave allowing for a complete spatial description of the instability wave to order unity. Calculations of the instability wave characteristics, near- and far-field pressure fluctuations for an unheated, ideally expanded, moderate Reynolds number jet with jet exit Mach number of 2.1 are performed at several frequencies and for the axisymmetric and helical instabilities. The numerical results of this model are then compared with experiments and good agreement is found in both the jet flow and near-field. / Source: Dissertation Abstracts International, Volume: 42-10, Section: B, page: 4099. / Thesis (Ph.D.)--The Florida State University, 1981.

An experimental study was carried out on Rayleigh-Benard convection in Couette flow in a horizontal annulus of water. Measurements of heat and momentum fluxes and observations of plan form were made in the low Rayleigh number (Ra) range from 5 $\times$ 10$\sp3$ to 8 $\times$ 10$\sp4$, and in the Reynolds number (Re) range of 10 to 90 to study the effect of shear on plan form and fluxes. Measurements of heat and momentum fluxes were made in the turbulent range of Rayleigh number from 2 $\times$ 10$\sp5$ to 5 $\times$ 10$\sp7$, and for Reynolds numbers in the range of 40 to 350 to study the effect of shear on momentum flux at high Rayleigh numbers. / In the low Rayleigh number range, with Reynolds numbers in the range from 35 to 86, longitudinal rolls are observed at low Rayleigh numbers and they become unstable as the Rayleigh number is increased. A previously unknown result is that the wave number of these longitudinal rolls increases as the Reynolds number is increased. Instabilities of longitudinal rolls are found to be both wavy and cross-roll. Wavy rolls with cross-roll disturbances are found to be stable in most of the parameter space for $Ra > 4\times 10\sp4$. Discrete slope increases in both the heat and momentum flux curves are observed at the transitions where the longitudinal rolls become unstable. / At high Rayleigh and Reynolds numbers, the Nusselt number (Nu) is observed to depend on Rayleigh number to the 0.33 $\pm$ 0.04 power. Curves of Nu vs Ra at high Re lie slightly below corresponding curves at lower Re. The dimensionless momentum flux (Mo) is observed to have different linear dependence upon Nusselt number in different parts within the parameter space. Curves of Mo vs Nu at high Re are well below curves at lower Re. Slopes of these curves decrease with increased Nusselt number and at the highest range of Rayleigh and Reynolds number, the slope becomes negative. / Source: Dissertation Abstracts International, Volume: 52-10, Section: B, page: 5170. / Major Professor: Ruby Krishnamurti. / Thesis (Ph.D.)--The Florida State University, 1991.

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A numerical investigation has been performed for the 3-D flow of an incompressible fluid in a torus shaped enclosure of square cross-section, where the fluid motion is induced by sliding the top wall of the enclosure radially outwards. The flow in this geometry is characterized by two non-dimensional numbers, the curvature ratio (δ=d/Rc) and the Reynolds number (Re=uwalld/v) where Rc is the radius of curvature of the torus at the center of the cavity, d is the side length of the enclosure cross-section and uwall the velocity of the top wall of the enclosure. Calculations were performed for 3-D flow in an almost straight enclosure with δ = 0.005 at Re = 3200 and a strongly curved one with δ = 0.25 at Re = 2400. The 3-D flow was computed by choosing a small sector of the torus and applying periodic boundary conditions along the circumferential boundary. The 3-D flow calculations were started with axi-symmetric flow as initial condition and perturbed by a small random disturbance to seed the centrifugal instability into the flow. Integral quantites defined using different components of the vorticity were monitored at different cross sectional planes to study the development and dynamics of the 3-D flow. A technique of volume visualization was used to visualize r vorticity and θ vorticity contours through out the computational domain to understand the dynamics of the 3-D flow. The 3-D flow calculated for both cases δ = 0.005 and 0.25 shows span-wise vortices also called Taylor-Gortler-Like vortices. These vortices while being convected around by the primary re-circulating flow in the torus cross-section experience span-wise oscillation resulting from a secondary instability accompanied by their growth and collapse in size. The net effect of this dynamics results in the periodic rearrangement of the vortices, when viewed along the circumferential span. Volume visualization of r-vorticity contours show the existence of two pairs of vortices wrapped around each other as they are convected around by the primary re-circulating flow. The dynamics that induce the periodic rearrangement have been explained from volume visualization of the vorticity components. "Vortex tilting" of theta-component of vorticity is identified as a mechanism for explaining the interaction of the primary re-circulating flow in the span-wise vortices present.

Analysis of the probability density functions (PDFs) of the velocity increment dvℓ and of their deformation is used to reveal the statistical structure of the intermittent energy cascade dynamics of turbulence. By analyzing a series of turbulent data sets including that of an experiment of fully developed low temperature helium turbulent gas flow (Belin, Tabeling, & Willaime, Physica D 93, 52, 1996), of a three-dimensional isotropic Navier-Stokes simulation with a resolution of 2563 (Cao, Chen, & She, Phys. Rev. Lett. 76, 3711, 1996) and of a GOY shell model simulation (Leveque & She, Phys. Rev. E 55, 1997) of a very big sample size (up to 5 billions), the validity of the Hierarchical Structure model (She & Leveque, Phys. Rev. Lett. 72, 366, 1994) for the inertial-range is firmly demonstrated. Furthermore, it is shown that parameters in the Hierarchical Structure model can be reliably measured and used to characterize the cascade process. The physical interpretations of the parameters then allow to describe differential changes in different turbulent systems so as to address non-universal features of turbulent systems. It is proposed that the above study provides a framework for the study of non-homogeneous turbulence. A convergence study of moments and scaling exponents is also carried out with detailed analysis of effects of finite statistical sample size. A quantity Pmin is introduced to characterize the resolution of a PDF, and hence the sample size. The fact that any reported scaling exponent depends on the PDF resolution suggests that the validation (or rejection) of a model of turbulence needs to carry out a resolution dependence analysis on its scaling prediction.

Plasmas are used extensively in the manufacturing of microelectronic devices. In typical fabrication facilities, plasmas may be used for etching, deposition, cleaning of a substrate, and chamber cleaning. One of the major challenges to the effective use of plasmas for microelectronics processing is the formation of particles and films from reaction byproducts, which can contaminate both the substrate and the chamber. However, in other communities, the growth of particles and films in plasmas provides opportunities for the production of novel materials, for studies of astrophysical phenomena, and for macroscopic simulations of condensed matter physics. Extensive studies of particles and films in plasmas have resulted in an understanding of particle dynamics including charging, trapping, transport, and deposition. However, comparatively little is understood about the nucleation and growth behavior of particles and films. In this contribution, particle and film formation mechanisms in low-pressure fluorocarbon plasmas are discussed. It is shown that gas phase molecular growth reactions are responsible for the formation of chemical precursor to particle and film nucleation. A fluorocarbon chemical reaction library has been developed, and when used in conjunction with a plasma chemical kinetics model, gives excellent agreement with experimental observations of molecular growth reactions and particle and film formation.

A transient axisymmetric model is developed to study the laser drilling phenomenon. Governing equations are the transient axisymmetric 3-D heat conduction equation for the solid substrate and for the liquid molten part, the thin layer model (TLM) equations are utilized. Boundary element method (BEM) is used for the region encompassing the moving boundary and finite difference method (FDM) is utilized for the remainder. BEM and FDM are coupled using flux and temperature at their interface. TLM is obtained using simplified free surface, mass, momentum and energy equations in body intrinsic coordinates. They are simplified by integrating across the layer using profiles for velocity and temperature thus obtaining a 1-D transient hyperbolic system. This is solved by a space-time flux conservation method. The TLM is coupled to the BEM-FDM by the common interface matching conditions. The constitutive equations governing laser interaction with material are used at the liquid-vapor interface.

A high-order immersed boundary method (IBM) for the computation of unsteady, incompressible fluid flows on two-dimensional, complex domains is proposed, analyzed, developed and validated. In the IBM, the equations of interest are discretized on a fixed Cartesian grid. As a result, domain boundaries do not always conform to the (rectangular) computational domain boundaries. This gives rise to 'immersed boundaries', i.e., boundaries immersed inside the computational domain. A new IBM is proposed to remedy problems in an older existing IBM that had originally been selected for use in numerical flow control investigations. In particular, the older method suffered from considerably reduced accuracy near the immersed boundary surface where sharp jumps in the solution, i.e., jump discontinuities in the function and/or its derivatives, were smeared out over several grid points. To avoid this behavior, a sharp interface method, originally developed by LeVeque & Li (1994) and Wiegmann & Bube (2000) in the context of elliptic PDEs, is introduced where the numerical scheme takes such discontinuities into consideration in its design. By comparing computed solutions to jump-singular PDEs having known analytical solutions, the new IBM is shown to maintain the formal fourth-order accuracy, in both time and space, of the underlying finite-difference scheme. Further validation of the new IBM code was accomplished through its application to several two-dimensional flows, including flow past a circular cylinder, and T-S waves in a flat plate boundary layer. Comparison of results from the new IBM with results available in the literature found good agreement in all cases.