Internal waves in the deep ocean play a deciding role in processes such as climate change and nutrient cycles. Winds and tidal currents over topography feed energy into internal waves at large scales; through nonlinear interaction the energy then cascades to turbulence scales and contributes to deep-ocean mixing. The connection of internal waves to deep-ocean mixing is what makes them important. In this thesis we address the problem of energy transfer in internal waves by modelling a two-dimensional flow over idealized topography and analysing the spectra of the generated wave fields. The main tool used is the nonparametric spectral analysis, some aspects of which are reviewed in one of the chapters. The numerical experiments were performed for a number of latitudes, topographies and background flows. The wave field generated by tide-topography interaction includes both progressive and trapped internal waves. The wave spectrum was found to exhibit a self-similar structure with prominent peaks at tidal harmonics and interharmonics, whose magnitudes decay exponentially as a function of the frequency. Subharmonics are generated by an instability of tidal beams, which is particularly strong for near-critical latitudes, where the Coriolis frequency is half the tidal frequency; other interharmonics are produced through resonant and non-resonant triad wave-wave interaction. As the triad interaction can be either resonant or non-resonant, some harmonics and interharmonics correspond to progressive waves, if the frequency is within the free internal wave range, while the others are trapped waves if the frequency is outside the range. Spatial scales of harmonics and interharmonics were investigated. In particular, it was shown that interharmonics typically have smaller vertical scales. Through the use of spatial analysis it was shown that there is a discrete number of wave-wave interactions responsible for the total energy transfer. The results of the thesis provide insight into the complex nature of internal wave interactions and may be helpful for interpreting recent observational results.

Internal waves in the deep ocean play a deciding role in processes such as climate change and nutrient cycles. Winds and tidal currents over topography feed energy into internal waves at large scales; through nonlinear interaction the energy then cascades to turbulence scales and contributes to deep-ocean mixing. The connection of internal waves to deep-ocean mixing is what makes them important. In this thesis we address the problem of energy transfer in internal waves by modelling a two-dimensional flow over idealized topography and analysing the spectra of the generated wave fields. The main tool used is the nonparametric spectral analysis, some aspects of which are reviewed in one of the chapters. The numerical experiments were performed for a number of latitudes, topographies and background flows. The wave field generated by tide-topography interaction includes both progressive and trapped internal waves. The wave spectrum was found to exhibit a self-similar structure with prominent peaks at tidal harmonics and interharmonics, whose magnitudes decay exponentially as a function of the frequency. Subharmonics are generated by an instability of tidal beams, which is particularly strong for near-critical latitudes, where the Coriolis frequency is half the tidal frequency; other interharmonics are produced through resonant and non-resonant triad wave-wave interaction. As the triad interaction can be either resonant or non-resonant, some harmonics and interharmonics correspond to progressive waves, if the frequency is within the free internal wave range, while the others are trapped waves if the frequency is outside the range. Spatial scales of harmonics and interharmonics were investigated. In particular, it was shown that interharmonics typically have smaller vertical scales. Through the use of spatial analysis it was shown that there is a discrete number of wave-wave interactions responsible for the total energy transfer. The results of the thesis provide insight into the complex nature of internal wave interactions and may be helpful for interpreting recent observational results.

In many engineering applications involving mixing of highly viscous fluids or mixing at micro-scales, efficient mixing must be accomplished in the absence of turbulence. Similarly in geophysical flows large-scale, deterministic flow structures can account for a considerable portion of global transport and mixing. For these types of problems, concepts from non-linear dynamical systems and the theory of chaotic advection provide the tools for understanding, quantifying, and optimizing transport and mixing processes. In this thesis chaotic advection is studied numerically in three, steady, experimentally realizable, three-dimensional flows: 1) steady vortex breakdown flow in a cylindrical container with bottom rotating lid, 2) flow in a cylindrical container with exactly counter rotating lids, and 3) flow in a new model stirred-tank with counter-rotating disks. For all cases the three-dimensional Navier-Stokes equations are solved numerically and the Lagrangian properties of the computed velocity fields are analyzed using a variety of computational and theoretical tools. For the flow in the interior of vortex breakdown bubbles it is shown that even though from the Eulerian viewpoint the simulated flow fields are steady and nearly axisymmetric the Lagrangian dynamics could be chaotic. Silnikovs mechanism is shown to play a critical role in breaking up the invariance of the bubble and giving rise to chaotic dynamics. The computations for the steady flow in a cylindrical container with two exactly counter-rotating lids confirm for the first time the findings of recent linear stability studies. Above a threshold Reynolds number the equatorial shear layer becomes unstable to azimuthal modes and an intricate web of radial (cats eyes) and axial, azimuthally-inclined vortices emerge in the flow paving the way for extremely complex chaotic dynamics. Using these fundamental insights, a new stirring tank device with exactly counter-rotating disks is proposed. Results show for the first time that counter rotation of the middle disk in a three-disk stirred tank can create a flow with large chaotic regions. The results of this thesis serve to demonstrate that fundamental studies of chaotic mixing are both important from a theoretical standpoint and can potentially lead to valuable technological breakthroughs.

Thesis (M.S.)--Missouri University of Science and Technology, 2010. / Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed Jan. 5, 2010). Includes bibliographical references (p. 52-53).

Thesis (Ph. D.)--Ohio State University, 2009. / Title from first page of PDF file. Includes bibliographical references (p. 239-251).

CFD simulations were used to study single phase and multiphase flows through structured packing. Simulations utilizing a high fidelity, digital copy of a packing element were validated against experimental results for both single phase and multiphase flows. Single phase simulations were carried out on a variety of periodic packing elements to examine the impact of packing channel geometry on pressure drop. Multiphase simulations on periodic elements were used to examine the effect of hydrodynamic properties and boundary conditions. Single-phase simulations of nitrogen flow through the high fidelity geometry produced via X-ray CT scans showed average deviations less than 15% when compared to experimental measurements. This error was reduced to 7% when a mesh utilizing prism layers to accurately resolve the boundary layer was used. With a validated model for single phase flow, the application of CFD to packing design was investigated on periodic geometries with varied packing parameters (e.g. channel corrugation angle and channel side length). It was found that current industrial packings have channel geometries maximizing pressure drop, indicating some degree of optimization around channel geometry is possible depending on separation needs. Multiphase simulations using the Volume of Fluid model examined the effects of liquid density, viscosity, surface tension, and contact angle on small-scale packing geometries. Contact angle had the most pronounced influence on predicted wetting, and simulations demonstrated that using experimentally determined static contact angles was not an appropriate choice for the simulation contact angle. The predicted influence of surface tension qualitatively matched experimental data for wetted area. Liquid viscosity and density also demonstrated qualitative agreement with semi-empirical models derived from experimental data. Experimental data collected via absorption of CO2 into 0.1 mol/L NaOH were compared to simulation predictions using a geometry generated via X-ray CT scans. Wetted area predictions matched experimental data best when a fully wetting static contact angle (0°) was used, yielding simulated results 3.4% lower than experimental data on average. Irrigated pressure drop and holdup predictions were significantly higher than experimental data. / text

published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy

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