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In this thesis I address several topics concerning the interaction of convection and density stratification in oceans and lakes. I present experimental and theoretical investigations of the interaction between a localized buoyancy source and a heat flux through a horizontal boundary, and of the interactions between salt fingers and intermittent turbulence or shear. ¶ An extensive series of laboratory experiments were used to quantify the stratification and circulation that result from the combined presence of a localized buoyancy source and a heat flux through a horizontal boundary. Previous studies found that convection in the form of a turbulent buoyant plume tends to produce a stable density stratification, whereas the distributed flux from a horizontal boundary tends to force vigorous overturning and to produce well-mixed layers. A new result of this thesis is that a steady density profile, consisting of a mixed layer and a stratified layer, can exist when the plume buoyancy flux is greater than the distributed flux. When the two fluxes originate from the same boundary, the steady state involves a balance between the rate at which the mixed layer deepens due to entrainment on the one hand and vertical advection of the stratified water far from the plume (due to the volume flux acquired by entrainment) on the other hand. There is a monotonic relationship between the normalized mixed layer depth and flux ratio R (boundary flux/plume flux) for 0 < R > 1, and the whole tank overturns for R > 1. The stable density gradient in the stratified region is primarily due to the buoyancy from the plume and for R > 0 there is a small increase in the gradient due to entrainment of buoyancy from the mixed layer. For the case of fluxes from a plume located at one boundary and a uniform heat flux from the opposite boundary the shape of the density profile is that given by Baines & Turner (1969), with the gradient reduced by a factor (1 + R) due to the heating. Thus, when R < - 1 there is no stratified region and the whole water column overturns. When 0 > R > - 1, the constant depth of the convecting layer is determined by the Monin-Obukhov scale in the outflow from the plume. ¶ One application of these laboratory experiments is to surface cooling in lakes and reservoirs that have shallow sidearms. During prolonged periods of atmospheric cooling, gravity currents can form in these sidearms and as the currents descend into the deeper waters they are analogous to isolated plumes. This can result in stratification at the base of a lake and an upwelling of cold water. Away from the shallow regions, surface cooling leads to a mixed surface layer. The depth of this layer will be steady when the rate of upwelling balances the rate at which the mixed layer deepens by turbulent entrainment. A series of laboratory experiments designed to model the depth distribution of a lake with a shallow sidearm showed that the steady depth of the mixed layer depended on the ratio of the area of the shallow region to the area of the deep region. Significant stratification resulted only when the reservoir had shallow regions that account for more than 50 % of the surface area. The depth of the surface mixed layer also depended on the ratio of the depths of the shallow and deep regions and no significant stratification forms if this ratio is greater than 0.5. These results are in good agreement with observations of circulation and stratification during long periods of winter cooling from Chaffey reservoir, Australia. Theoretical time scales are also developed to predict the minimum duration of atmospheric cooling that can lead the development of stratification. ¶ In the second part of this thesis, I report a series of laboratory experiments which are designed to investigate the fine structure and buoyancy fluxes that result from salt finger convection in the presence of shear and intermittent turbulence. We find that, when salt finger convection in deep linear gradients is superposed with a depth-dependent spatially periodic shear, variations in the density profile develop on the same wavelength as the shear. The laboratory experiments presented in this thesis were carried out in a continuous density gradient with a spatially periodic shear produced by exciting a low-frequency baroclinic mode of vertical wavelength 60 mm. The density gradient consisted of opposing salt and sugar gradients favourable to salt fingers (an analogue to the oceanic heat/salt system). Where the shearing was large the salt finger buoyancy fluxes were small. Changes in salinity gradient due to the resulting flux divergence were self-amplifying until a steady state was reached in which the spatial variations in the ratio of salt and sugar gradients were such that the flux divergence vanished. Thus, along with reducing the mean salt finger buoyancy flux, a spatially varying shear can also lead to the formation of density structure. ¶ In the ocean intermittent turbulence can occur in isolated patches in salt finger-favourable regions. I present new results from laboratory experiments in which a partially mixed patch was produced in deep linear concentration gradients favourable to salt finger convection. Salt fingers give rise to an “up gradient” flux of buoyancy which can reduce the density gradient in a partially mixed patch. This can then lead to overturning convection of the partially mixed patch if a) the ratio of T and S gradients, R\rho =aTz/_ /betaSz, is near one, b) if turbulence results in a nearly well-mixed patch and c) the patch thickness is large enough that convective eddies are able to transport T and S faster than salt fingers. Once overturning occurs, subsequent turbulent entrainment can lead to growth of the patch thickness. Experimental results agree well with the theoretical prediction that h= \surd 8h B/N2 t, where h is the patch thickness, t is time, h is the mixing efficiency of turbulent entrainment, B is the buoyancy flux of the salt fingers and N is the buoyancy frequency of the ambient gradient region. This thickening is in contrast to the collapse that a partially mixed patch would experience due to lateral intrusion in a very wide tank. In regions of the ocean that contain salt fingers there is the possibility that, after a period of initial collapse, an intrusion could enter a regime where the rate of collapse in the vertical is balanced by the growth rate due to turbulent entrainment from the salt fingers buoyancy flux, thus tending to maintain the rate of lateral spread. ¶ A further series of laboratory experiments quantified the buoyancy fluxes that result from salt fingers and intermittent turbulence. A continuous density gradient, favourable to salt finger convection, was stirred intermittently by an array of vertical rods that move horizontally back and forth along the tank at a constant velocity. Previous experiments had found that continuous turbulence destroys any salt fingers present because the dissipation of turbulent kinetic energy occurs at scales that are generally smaller than salt fingers widths. However, when turbulence is present only intermittently, the salt fingers may have time to grow between turbulent events and so contribute to the vertical diffusivities of heat and salt. We conclude that the vertical buoyancy flux of salt fingers is strongly dependent upon the intermittency of the turbulence, and equilibrium fluxes are only achieved if the time between turbulent events is much greater than the e-folding time of the salt fingers. When these results are applied to an oceanographic setting, the effect of intermittent turbulence, occurring more 5% of the time, is to reduce the effective eddy diffusivity due to salt fingers below equilibrium salt finger values, so that at R\rho > > 2 the eddy diffusivity is due only to turbulence. The time averaged salt fingers fluxes are not significantly reduced by intermittent turbulence when R\rho > 2 or if the intermittence occurs less than 2% of the time, and so may contribute significant diapycnal fluxes in many parts of the ocean.

Several types of instability can affect the interface between two fluids. For instance, a Rayleigh-Taylor instability (or density fingering) is encountered when a heavier fluid is placed upon a lighter one in the gravity field and double diffusive instabilities can be triggered by differential diffusivity of the different species present in the fluid. In this context our work aims to understand theoretically in which way a chemical reaction can induce and influence such instabilities in a fluid initially at rest. To understand the dynamics resulting from the coupling between chemical reactions and hydrodynamical instabilities we use chemical fronts as model systems. These fronts result from the coupling between autocatalytical chemical reactions and diffusion and they allow to create a self-organized interface between the products and the reactants. As during a chemical reaction the density may vary due to solutal and thermal effects, the products and the reactants can have different densities which may trigger convection movements leading to the destabilization of the fronts. We have in particular studied the influence of the exothermicity of the reaction on the fingering of chemical fronts, focusing first on the influence of heat losses through the walls of the set-up. These leaks have a marked influence on the dynamics because they affect the temperature profiles and hence the density profiles too. We have also classified the various types of instabilities that may appear dues to solutal and thermal effects. We have found a new type of hydrodynamic instability of statically stable fronts induced by the chemical reaction. We have furthermore analyzed an isothermal model with two chemical species. If they diffuse at different rates the front can be subject to diffusive instabilities as well. We have shown that the coupling between such a diffusive instability and fingering can trigger complex dynamics. We have eventually studied the influence of an external electric field on the diffusive instabilities and on fingering underlying the possibility to destabilize otherwise stable fronts./ Différents types d'instabilités hydrodynamiques peuvent affecter les interfaces entre deux fluides comme par exemple, une instabilité de Rayleigh-Taylor (ou digitation de densité) quand un fluide plus dense se trouve placé au-dessus d'un fluide moins dense dans le champ de gravité ou des instabilités de double diffusion induites par des différences entre les diffusivités d'un soluté et de la chaleur contenus dans les fluides. Dans ce contexte, notre thèse s'attache à comprendre de manière théorique comment une réaction chimique peut influencer ces instabilités voire les générer dans un fluide initialement au repos. Pour étudier les dynamiques résultant du couplage entre réactions chimiques et instabilités hydrodynamiques, nous utilisons des systèmes modèles: les fronts chimiques de conversion résultant de la compétition entre réactions chimiques autocatalytiques et diffusion créant une interface auto-organisée entre les réactifs et les produits. Comme au cours d'une réaction chimique la densité peut varier par des effets solutaux et thermiques, les produits et les réactifs de densités différentes peuvent générer des mouvements de convection qui conduisent à la déstabilisation des fronts. Nous avons en particulier étudié l'influence de l'exothermicité de la réaction sur les instabilités de digitation de fronts chimiques, en nous focalisant dans un premier temps sur l'influence des pertes de chaleur par les parois du réacteur. Ces fuites ont un effet marqué sur les instabilitités car elles affectent les profils de température et donc les profils de densité dans le système. Nous avons également classifié les différentes instabilités qui peuvent apparaître via des changements de densité dûs à des effets thermiques et solutaux et mis en évidence un nouveau type de déstabilisation hydrodynamique de fronts statiquement stables induit par une réaction chimique. Nous avons ensuite analysé un modèle isotherme impliquant deux espèces chimiques. Si ces dernières diffusent a des vitesses différentes le front peut être sujet à une instabilité diffusive. Nous avons montré qu'un couplage entre une telle instabilité diffusive et de la digitation peut être à l'origine de dynamiques complexes. Nous avons ensuite considéré l'influence d'un champ électrique sur les instabilité diffusives et de digitation en soulignant la possibilié de déstabiliser via ce champ des fronts initialement stables.

The permeability of cell membranes varies significantly across both healthy and diseased tissue, and changes in cell membrane permeability can occur during treatment response in tumours. Measurements of cell membrane permeability could therefore be useful for tumour detection and as biomarkers of treatment response in the clinic. As the diffusion of water across the cell membrane is directly dependent on cell membrane permeability, we have investigated the ability of diffusion-diffusion exchange spectroscopy to quantify the diffusion exchange of water in a suspension of yeast, as a first step towards its application in tumours.

Measuring transmembrane water exchange can provide potential biomarkers for tumors and brain disorders. Diffusion Magnetic Resonance Imaging (dMRI) is a well-established tool that can non-invasively measure water exchange across cell membranes. Diffusion Exchange Spectroscopy (DEXSY) is one of the dMRI-based frameworks used to estimate exchange. DEXSY provides a detailed picture of multi-site exchange processes but requires a large quantity of data. Several models based on the DEXSY framework have been proposed to reduce the acquisition time. Filter Exchange Imaging (FEXI) and curvature models are two of them that only require certain samples of the DEXSY dataset. Diffusion-Exchange Weighted (DEW) Imaging model is another data reduction method accounting for restricted diffusion within cells and can use a specific subset of the DEXSY dataset to measure exchange. Furthermore, a more general expression of the DEXSY signal, referred to as the general model, can theoretically analyze the full space or reduced DEXSY datasets and estimate exchange. However, the results of the subsampling schemes and the data reduction models have not been compared to the full space estimation.  Therefore, this thesis aims to experimentally explore the feasibility of estimating exchange using these four models (the general, FEXI, curvature and DEW models) with the data acquired using a low-field benchtop MR scanner, and compare the estimates from the general model with different subsampling schemes and the data reduction models to the full space estimation. For this purpose, a double diffusion encoding (DDE) sequence was modified from an existing sequence on the benchtop MR scanner and a DEXSY experiment was conducted on this MR scanner and a yeast phantom to acquire a full space dataset. The exchange parameters estimated from the full space dataset using the general model were used as "ground truths" to evaluate the estimates from the reduced datasets analyzed using the general, FEXI and curvature models. Moreover, two alternative subsampling schemes named the shifted DEW and new trajectory schemes were proposed and employed to measure exchange. The results indicate that all the methods except the curvature sampling scheme employed with both the general and curvature models provided comparable estimates to the "ground truths". The shifted DEW and new trajectory sampling schemes performed better over others in terms of consistency with the "ground truths" and low variations between voxels, suggesting the theoretical and experimental optimization of these two subsampling schemes can be further studied and developed.

Several types of instability can affect the interface between two fluids. For instance, a Rayleigh-Taylor instability (or density fingering) is encountered when a heavier fluid is placed upon a lighter one in the gravity field and double diffusive instabilities can be triggered by differential diffusivity of the different species present in the fluid. <p>In this context our work aims to understand theoretically in which way a chemical reaction can induce and influence such instabilities in a fluid initially at rest.<p>To understand the dynamics resulting from the coupling between chemical reactions and hydrodynamical instabilities we use chemical fronts as model systems. These fronts result from the coupling between autocatalytical chemical reactions and diffusion and they allow to create a self-organized interface between the products and the reactants. As during a chemical reaction the density may vary due to solutal and thermal effects, the products and the reactants can have different densities which may trigger convection movements leading to the destabilization of the fronts.<p><p>We have in particular studied the influence of the exothermicity of the reaction on the fingering of chemical fronts, focusing first on the influence of heat losses through the walls of the set-up.<p>These leaks have a marked influence on the dynamics because they affect the temperature profiles and hence the density profiles too. We have also classified the various types of instabilities that may appear dues to solutal and thermal effects. We have found a new type of hydrodynamic instability of statically stable fronts induced by the chemical reaction. <p><p>We have furthermore analyzed an isothermal model with two chemical species. If they diffuse at different rates the front can be subject to diffusive instabilities as well. We have shown that the coupling between such a diffusive instability and fingering can trigger complex dynamics. We have eventually studied the influence of an external electric field on the diffusive instabilities and on fingering underlying the possibility to destabilize otherwise stable fronts./<p>Différents types d'instabilités hydrodynamiques peuvent affecter les interfaces entre deux fluides comme par exemple, une instabilité de Rayleigh-Taylor (ou digitation de densité) quand un fluide plus dense se trouve placé au-dessus d'un fluide moins dense dans le champ de gravité ou des instabilités de double diffusion induites par des différences entre les diffusivités d'un soluté et de la chaleur contenus dans les fluides. Dans ce contexte, notre thèse s'attache à comprendre de manière théorique comment une réaction chimique peut influencer ces instabilités voire les générer dans un fluide initialement au repos. Pour étudier les dynamiques résultant du couplage entre réactions chimiques et instabilités hydrodynamiques, nous utilisons des systèmes modèles: les fronts chimiques de conversion résultant de la compétition entre réactions chimiques autocatalytiques et diffusion créant une interface auto-organisée entre les réactifs et les produits. Comme au cours d'une réaction chimique la densité peut varier par des effets solutaux et thermiques, les produits et les réactifs de densités différentes peuvent générer des mouvements de convection qui conduisent à la déstabilisation des fronts. <p><p>Nous avons en particulier étudié l'influence de l'exothermicité de la réaction sur les instabilités de digitation de fronts chimiques, en nous focalisant dans un premier temps sur l'influence des pertes de chaleur par les parois du réacteur.<p>Ces fuites ont un effet marqué sur les instabilitités car elles affectent les profils de température et donc les profils de densité dans le système. Nous avons également classifié les différentes instabilités qui peuvent apparaître via des changements de densité dûs à des effets thermiques et solutaux et mis en évidence un nouveau type de déstabilisation hydrodynamique de fronts statiquement stables induit par une réaction chimique. <p>Nous avons ensuite analysé un modèle isotherme impliquant deux espèces chimiques. Si ces dernières diffusent a des vitesses différentes le front peut être sujet à une instabilité diffusive. Nous avons montré qu'un couplage entre une telle instabilité diffusive et de la digitation peut être à l'origine de dynamiques complexes. Nous avons ensuite considéré l'influence d'un champ électrique sur les instabilité diffusives et de digitation en soulignant la possibilié de déstabiliser via ce champ des fronts initialement stables. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Doppelt diffusive Konvektion im Fingerregime wurde mittels einer elektrochemischen Zelle untersucht. Kupferionen bilden die destabilisierende und Temperatur die stabilisierende Komponente. In diesen System existieren Finger und thermohaline Treppen, obwohl die Gesamtdichtestratifizierung instabil ist. Fingerströmung wird durch Konvektionsrollen ersetzt, wenn die Konvektion schnell genug ist um Temperaturdiffusion zwischen den Fingern zu unterbinden, bzw. wenn die thermische Auftriebskraft 1/30 der chemischen Auftriebskraft beträgt. Am Übergang ist der Ionentransport größer, als ohne stabilisierenden Temperaturgradienten.

Double diffusive phenomena occur in many natural systems and in a variety of engineering applications, such as solar ponds. In a solar pond, the erosion of gradient zone due to convection and diffusion is the main cause of inefficiency and hence, requires lot of maintenance. In this thesis, control of erosion of the gradient zone in a solar pond situation has been studied through experiments and transient numerical simulations. A laboratory solar pond was setup in a tank of size 19cm X 19cm X 19cm, and was heated from below. A polymer additive, Carboxy Methyl Cellulose (CMC) was used to increase the viscosity of the working fluid. With 0.01% CMC, viscosity enhancement of the working fluid by 25 to 30 times was achieved, without changing any other properties. The transient momentum, energy and species conservation equations along with continuity equation were solved numerically, using the SIMPLER algorithm with 2 mm grid spacing. The experiments conducted with the addition of CMC, showed delays in the onset of convection and reduced erosion of the gradient zone. The erosion rates obtained from the numerical simulations agreed with the experimental observation. The impact of viscosity on the onset of convection, kinetic energy, convection pattern, frequency of bursts and erosion rate of the gradient zone, were simulated. Numerical simulations revealed that, there is a nonlinear relationship between the viscosity and erosion rate of the gradient zone. Increase in viscosity by a factor of 15 reduced the erosion of gradient zone completely, indicating the dominant role played by Turbulent entrainment. The present work indicates that the control of erosion of gradient zone in solar pond using the polymer additive shows lot of promise. The use of the polymer additive as a method to increase viscosity will lower the maintenance costs and, increase the reliability and efficiency of solar ponds, with less than 5% increase in the initial cost.

Ce travail concerne la convection naturelle au sein d'un système fluide-poreux en couche horizontale. On présente l'analyse de stabilité linéaire des modèles à un et deux domaines, avec diffusion visqueuse dans le milieu poreux. Nos résultats sont comparés avec ceux du modèle à deux domaines utilisant la formulation de Darcy. Un bon accord est observé entre les résultats des modèles à deux domaines, ce qui indique que le terme de Brinkman joue un rôle secondaire dans la stabilité. On montre que le modèle à un domaine peut conduire à des résultats sensiblement différents lorsque la transition entre fluide et le milieu poreux est décrite par une discontinuité des propriétés. Il faut alors modifier la formulation en effectuant la différentiation au sens des distributions. Ainsi, le modèle à un domaine conduit aux mêmes seuils de stabilité que les formulations à deux domaines. L'influence des paramètres caractéristiques sur la stabilité des systèmes thermique et thermosolutal est discutée.

Dans cette thèse, les transferts de chaleur et de masse par convection naturelle en<br />milieux fluides et poreux ont été étudiés numériquement. Les parois verticales sont<br />soumises à des températures et concentrations constantes, tandis que les parois<br />horizontales sont adiabatiques et imperméables. Le phénomène de la convection<br />thermosolutale est régi par les équations de conservation de la masse, de la quantité de<br />mouvement, de l'énergie et de la concentration. le milieu poreux est modélisé suivant le<br />modèle général de Darcy – Brinkman – Forchheimer. L'écoulement convectif est régi par<br />différents paramètres de contrôle, à savoir le nombre de Rayleigh (Ra), le rapport des<br />forces de volume (N), le nombre de Prandtl(Pr), le nombre de Lewis (Le), le nombre de<br />Darcy (Da) et la porosité ε de la matrice poreuse. La méthode des volumes de contrôle a<br />été employée pour résoudre les équations de base en milieux fluide et poreux. Concernant<br />la validation du code de calcul, l'accord obtenu entre nos résultats et ceux disponibles<br />dans la littérature s'est avéré excellent. L'influence des paramètres physiques et<br />géométriques est examinée. L'augmentation de l'épaisseur de la couche poreuse de faible<br />perméabilité réduit considérablement les transferts thermique et massique. La<br />décroissance du transfert de chaleur avec l'accroissement du rapport des forces de volume<br />à nombre de Lewis élevé est mise en évidence. Par ailleurs, dans un souci de mettre à la<br />disposition de l'ingénieur un outil lui permettant d'évaluer les transferts thermiques et<br />massiques ayant lieu dans une configuration de type considérée, des corrélations sont<br />proposées.