<p> An experimental study of stratified fluid flow phenomena for two equal depth, different density stratified liquids in a rectangular channel is presented. Two two fluid combinations were used, a sugar water and fresh water, and fresh water and varsol. The critical value of the determined densimetric Froude number at which the upper fluid began to participate in the flow was obtained and found to be 0.28 as against Huber's (1) predicted value of 2.76. It was concluded that the interfacial mixing and viscous effects are largely responsible for this difference. </p> <p> An attempt to extend Harleman's (7) work was made. The results obtained in present work were in good agreement with Harleman's (7) experimental work. </p> / Thesis / Master of Engineering (ME)

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<p>This thesis, consisting of three papers and a summary, studies properties of stratified algebras and representations of Lie superalgebras.</p><p>In Paper I we give a characterization when the Ringel dual of an SSS-algebra is properly stratified.</p><p>We show that for an SSS-algebra, whose Ringel dual is properly stratified, there is a (generalized) tilting module which allows one to compute the finitistic dimension of the SSS-algebra, and moreover, it gives rise to a new covariant Ringel-type duality.</p><p>In Paper II we give a characterization of standardly stratified algebras in terms of certain filtrations of (left or right) projective modules, generalizing the corresponding theorem of V. Dlab. We extend the notion of Ringel duality to standardly stratified algebras and estimate their finitistic dimension in terms of endomorphism algebras of standard modules.</p><p>Paper III deals with the queer Lie superalgebra and the corresponding BGG-category O. We show that the typical blocks correspond to standardly stratified algebras, and we generalize Kostant's Theorem to the queer Lie superalgebra.</p>

This thesis, consisting of three papers and a summary, studies properties of stratified algebras and representations of Lie superalgebras. In Paper I we give a characterization when the Ringel dual of an SSS-algebra is properly stratified. We show that for an SSS-algebra, whose Ringel dual is properly stratified, there is a (generalized) tilting module which allows one to compute the finitistic dimension of the SSS-algebra, and moreover, it gives rise to a new covariant Ringel-type duality. In Paper II we give a characterization of standardly stratified algebras in terms of certain filtrations of (left or right) projective modules, generalizing the corresponding theorem of V. Dlab. We extend the notion of Ringel duality to standardly stratified algebras and estimate their finitistic dimension in terms of endomorphism algebras of standard modules. Paper III deals with the queer Lie superalgebra and the corresponding BGG-category O. We show that the typical blocks correspond to standardly stratified algebras, and we generalize Kostant's Theorem to the queer Lie superalgebra.

Density stratification is one of the essential underlying physical mechanisms for atmospheric and oceanic flow. As a first step to investigating the mechanisms of stratified turbulence, linear stability plays a critical role in determining under what conditions a flow remains stable or unstable. In the study of transition to stratified turbulence, a common vortex model, known as the Lamb-Chaplygin dipole, is used to investigate the conditions under which stratified flow transitions to turbulence. Numerous investigations have determined that a critical length scale, known as the buoyancy length, plays a key role in the breakdown and transition to stratified turbulence. At this buoyancy length scale, an instability unique to stratified flow, the zigzag instability, emerges. However investigations into sub-buoyancy length scales have remained unexplored. In this thesis we discover and investigate a new instability of the Lamb-Chaplyin dipole that exists at the sub-buoyancy scale. Through numerical linear stability analysis we show that this short-wave instability exhibits growth rates similar to that of the zigzag instability. We conclude with nonlinear studies of this short-wave instability and demonstrate this new instability saturates at a level proportional to the cube of the aspect ratio.

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[Truncated abstract] Internal waves redistribute energy and momentum in stratified lakes and constitute the path through which the energy that is introduced at the lake scale is cascaded down to the turbulent scales where mixing and dissipation take place. This research, based on intensive field data complemented with numerical simulations, covers several aspects of the energy flux path ranging from basin-scale waves with periods of several hours to high frequency waves with periods of few minutes. It was found that, at the basin-scale level, the horizontal shape of the lake at the level of the metalimnion controls the period and modal structure of the basin-scale natural modes, conforming to the dispersion relationship of internal waves in circular basins. The sloping bottom, in turn, produces local intensification of the wave motion due to focusing of internal wave rays over near-critical slopes, providing hot spots for the degeneration of the basin-scale waves due to shear instabilities, nonlinear processes and dissipation. Different types of high-frequency phenomena were observed in a stratified lake under different forcing conditions. The identification of the generation mechanisms revealed how these waves extract energy from the mean flow and the basin-scale waves. The changes to the stratification show that such waves contribute to mixing in different ways . . . Detailed field observations were used to develop a comprehensive description of an undocumented energy flux mechanism in which shear-instabilities with significant amplitudes away from the generation level are produced in the surface layer due to the shear generated by the wind. The vertical structure of these instabilities is such that the growing wave-related fluctuations strain the density field in the metalimnion triggering secondary instabilities. These instabilities also transport energy vertically to the thermocline where they transfer energy back to the mean flow through interaction with the background shear.

Vita. / Digitized by Kansas Correctional Industries

The Rayleigh-Taylor instability is a buoyancy driven instability that takes place in a stratified fluid system with a constant acceleration directed from the heavy fluid into the light fluid. In this study, both experimental data and numerical simulations are presented. Experiments are performed primarily using a lithium-tungstate aqueous solution as the heavy liquid, but sometimes a calcium nitrate aqueous solution is used for comparison purposes. Experimental data is obtained for both miscible and immiscible fluid combinations. For the miscible experiments the light liquid is either ethanol or isopropanol, and for the immiscible experiments either silicone oil or trans-anethole is used. The resulting Atwood number is either 0.5 when the lithium-tungstate solution is used or 0.2 when the calcium nitrate solution is used. These fluid combinations are either forced or left unforced. The forced experiments have an initial perturbation imposed by vertically oscillating the liquid containing tank to produce Faraday waves at the interface. The unforced experiments rely on random interfacial fluctuations, due to background noise, to seed the instability. The liquid combination is partially enclosed in a test section that is accelerated downward along a vertical rail system causing the Rayleigh-Taylor instability. Accelerations of approximately 1g (with a weight and pulley system) or 10g (with a linear induction motor system) are experienced by the liquids. The tank is backlit and digitally recorded with high speed video cameras. These experiments are then simulated with the incompressible, Navier-Stokes code Miranda. The main focus of this study is the growth parameter (ɑ) of the mixing region produced by the instability after it has become apparently self-similar and turbulent. The measured growth parameters are compared to determine the effects of miscibility and initial perturbations (of the small wavelength, finite bandwidth type used here). It is found that while initial perturbations do not affect the instability growth, miscibility does.

Stably stratified flows are common in the environment such as in the atmospheric· boundary layer, the oceans, lakes and estuaries. Understanding mixing and dispersion in these flows is of fundamental importance in applications such as the prediction of pollution dispersion and for weather and climate prediction/models. Mixing efficiency in stratified flows is a measure of the proportion of the turbulent kinetic energy that goes into increasing the potential energy of the fluid by irreversible mixing. This can be important for parameterizing the effects of mixing in stratified flows. In this research, fully resolved direct numerical simulations (DNS) of the Navier-Stokes equations are used to study transient turbulent mixing events. The breaking of internal waves in the atmosphere could be a source of such episodic events in the environment. The simulations have been used to investigate the mixing efficiency (integrated over the duration of the event) as a function of the initial turbulence Richardson number Ri = N2L2/U2, where N is the buoyancy frequency, L is the turbulence length scale, and u is the turbulence velocity scale. Molecular effects on the mixing efficiency have been investigated by varying the Prandtl number Pr = V/K, where v is the viscosity and K is the scalar diffusivity. Comparison of the DNS results with grid turbulence experiments has been carried out. There is broad qualitative agreement between the experimental and DNS results.· However the experiments suggest a maximum mixing efficiency of 6% while our DNS gives values about five times higher. Reasons for this discrepancy are investigated. The mixing efficiency has also been determined using linear theory. It is found that the results obtained for the very stable cases converge on those obtained from DNS suggesting that strongly stratified flows exhibit linear behaviour. Lagrangian analysis of mixing is fundamental in understanding turbulent diffusion and mixing. Dispersion models such as that of Pearson, Puttock & Hunt (1983) are based on a Lagrangian approach. A particle-tracking algorithm (using a cubic spline interpolation scheme following Yeung &Pope, 1988) was developed and incorporated into the DNS code to enable an investigation into the fundamental aspects of mixing and diffusion from a Lagrangian perspective following fluid elements. From the simulations, the ensemble averaged rate of mixing as a function of time indicates clearly that nearly all the mixing in these flows occurs within times of order 3 Vu. The mean square vertical displacement statistics show how the stable stratification severely inhibits the vertical displacement of fluid elements but has no effect on displacements in the transverse direction. This is consistent with the Pearson, Puttock & Hunt model. The important link that asymptotic value of the mean square vertical displacement is a measure of the total irreversible mixing that has occurred in the flow is made. However the results show that the change in density of the fluid elements is only weakly correlated to the density fluctuations during the time when most of the mixing occurs, which contradicts a key modeling assumption of the PPH theory. Improvements to the parameterization of this mixing are investigated. Flow structures in stably stratified turbulence were examined using flow visualization software. The turbulence structure for strong stratification resembles randomly scattered pancakes that are flattened in the horizontal plane. It appears that overturning motions are the main mechanism by which mixing occurs in these flows. / Thesis (M.Sc.Eng.)-University of Natal, Durban, 2002.