An experimental study of the effect of initial conditions on the development of Rayleigh Taylor Instabilities (RTI) at low Atwood numbers (order of 10-4) was performed in the water channel facility at TAMU. Initial conditions of the flow were generated using a controllable, highly reliable Servo motor. The uniqueness of the study is the system’s capability of generating the required initial conditions precisely as compared to the previous endeavors. Backlit photography was used for imaging and ensemble averaging of the images was performed to study mixing width characteristics in different regimes of evolution of Rayleigh-Taylor Instability (RTI). High-speed imaging of the flows was performed to provide insights into the growth of bubble and spikes in the linear and non-linear regime of instability development. RTI are observed in astrophysics, geophysics and in many instances in nature. The vital role of RTI in the feasibility and efficiency of the Inertial Confinement Fusion (ICF) experiment warrants a comprehensive study of the effect of mixing characteristics of RTI and its dependence on defining parameters. With this broader objective in perspective, the objectives of this present investigation were mainly threefold: First was the validation of the novel setup of the Water channel system. Towards this objective, validation of Servo motor, splitter plate thickness effects, density and temperature measurements and single-mode experiments were performed. The second objective was to study the mixing and growth characteristics of binary and multi-mode initial perturbations seeking an explanation of behavior of the resultant flow structures by performing the first ever set of such highly controlled experiments. The first-ever set of experiments with highly controlled multi-mode initial conditions was performed. The final objective of this study was to measure and compare the bubble and spike velocities with single-mode initial conditions with existing analytical models. The data derived from these experiments would qualitatively and quantitatively enhance the understanding of dependence of mixing width on parametric initial conditions. The knowledge would contribute towards a generalized theory for RTI mixing with specified dependence on various parameters, which has a wide range of applications. The system setup was validated to provide a reliable platform for the novel multi-modal experiments to be performed in the future. It was observed that the ensemble averaged mixing width of the binary system does not vary significantly with the phase-difference between the modes of a binary mode initial condition experiment, whereas it varies with the amplitudes of the component modes. In the exponential and non-linear regimes of evolution, growth rates of multi-mode perturbations were found to be higher than the component modes, whereas saturation growth rates correspond to the dominant wavelength. Quadratic saturation growth rate constants, alpha were found to be about 0.07 ± 0.01 for binary and multi modes whereas single-mode data measured alpha about 0.06 ± 0.01. High-speed imaging was performed to measure bubble and spike amplitudes to obtain velocities and growth rates. It was concluded that higher temporal and spatial resolution was required for accurate measurement. The knowledge gained from the above study will facilitate a better understanding of the physics underlying Rayleigh-Taylor instability. The results of this study will also help validating numerical models for simulation of this instability, thereby providing predictive capability for more complex configurations.

Cette thèse propose un éclairage sur la réalité de la Fonction analytique, sa physiologie, et les pathologies comportementales qui résultent de son dysfonctionnement. Nous y visitons les travaux de Freud, Jung et Lacan. Par une approche de comparatisme de leurs « écritures respectives », nous découvrons les fondements de la Fonction analytique. Tous trois tiennent leur savoir d’une approche transdisciplinaire (mythologie, alchimie, Taoïsme, linguistique, mathématiques, etc.) Freud précise le rôle indispensable de la pulsion en décrivant ses quatre caractéristiques. Avec son travail sur le «Bloc-notes magique », il énonce les modalités de la gravure psychique. La physiologie analytique comprend deux stades distincts : le premier ou « tronc commun » correspond à la gravure de la trace mnésique (Freud). Ce stade se déroule selon le mode binaire : ça pour Freud, persona pour Jung, imaginaire pour Lacan. Le second, se développe à partir du tronc commun, selon la modalité ternaire : la structure arborescente. C’est le stade du moi de Freud, du moi de Jung, du réel de Lacan. Cette phase, comme celle du brassage inter-chromosomique de la méiose biologique, produit une infinité de combinaisons. Modes binaire et ternaire représentent les phases principales de la Fonction analytique. Mais le mode binaire ne doit pas faire barrage au mode ternaire, en enfermant la psyché dans l’imaginaire (Lacan). La psyché doit se dépasser et faire oeuvre d’artiste. Nous montrons que le déséquilibre de l’archétype anima/animus (Jung) est cause de ces pathologies. Nous y voyons également que « la pensée judéo-chrétienne » joue un rôle de censeur, et fait obstacle à la modélisation ternaire. / The following thesis proposes to shed some light on the reality of Analytical Function, its physiology and the behavioural pathologies that derive from its dysfunction. We revisit the works of Freud, Jung and Lacan. Through a comparativistic approach of their “respective writings”, we discover the very fundamentals of Analytical Function. And all three had gathered their knowledge using a transdisciplinary approach (mythology, alchemy, Taoism, linguistics, mathematics etc…) Freud points out the main role of the drive by describing its four characteristics. In his “Magic Note Pad” he states the modalities of the psychic imprint. Analytical physiology comprises two distinct stages: the first one - “the common trunk”- refers to the imprint or engraving of the mnemonic marking. This stage unfolds according to a binary mode: the “It” for Freud, the “persona” for Jung and the “Imaginary” for Lacan. The second stage stems out of the common trunk on a ternary mode: the arborescent structure. This is the stage of the “I” for Freud, the “Self” for Jung and “the Real” for Lacan. This stage-just like the inter-chromosomal brew of the biological meiosis- produces an infinity of combinations. Binary and ternary modes represent the main phases of Analytical Function. Nevertheless the binary mode must not block out the ternary mode by locking the psyche into Lacan’s “Imaginary”. The psyche must go beyond itself and become its own artist. We show that the disequilibrium of Jung’s anima/animus archetype provokes these pathologies. We also notice that the “Judeo-Christian” way of thinking plays a censorship role and becomes an obstacle for the implementation of the ternary mode.