This study investigates the turbulent mixing within gravity currents preceding backdrafts and validates the ability of the computational fluid dynamics (CFD) software Fire Dynamics Simulator version 4 (FDS) to simulate these flows. Backdrafts are rapid deflagrations, which occur after the introduction of oxygen into compartments containing unburned gaseous fuel. They may form large fireballs out of the compartment opening and present a significant hazard to the safety of fire-fighters. Gravity currents which precede backdrafts are responsible for the formation of flammable gas mixtures required for ignition. Scale saltwater modelling is used to generate Boussinesq, fully turbulent gravity currents for five different opening geometries, typical of fire compartments. Width-integrated concentration fields and two-dimensional velocity fields are generated using the non-intrusive light attenuation (LA) and particle tracking velocimetry (PTV) flow visualisation techniques respectively. Numerical simulations are carried out with FDS to replicate these flows. The experimental and numerical results are compared directly. Front velocities are shown to be governed directly by local buoyancy conditions, in the later stages of the flows, and therefore the initial conditions associated with the opening geometries only influence the front velocities indirectly. The internal concentration structure, internal velocity structure and location of potential flammable regions are found to be highly opening geometry dependent. In general, the results of the numerical simulations are quantitatively similar to those from experiment, which suggests that the numerical model realistically predicted the experimental flows. However, the numerical concentration fields appear slightly lumpier than those from the experiments, possibly due to unresolved turbulence on scales smaller than the numerical grid (0.01H, where H = compartment height).

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.

Mixing between overflows and ambient water masses is a crucial problem of deep-water formation in the down-welling branch of the meridional overturning circulation of the ocean. In this dissertation work, performance of second-order turbulence closures in reproducing mixing of overflows is investigated within both hydrostatic and non-hydrostatic models. First, a 2D non-hydrostatic model is developed to simulate the Red Sea overflow in the northern channel. The model results are compared to the Red Sea Outflow Experiment. It is found that the experiments without sub-grid scale models cannot reproduce the basic structure of the overflow. The k-ε model yields unrealistically thick bottom layer (BL) and interfacial layer (IL). A new technique so-called very large eddy simulation (VLES) which allows the use of k-ε model in non-hydrostatic models is also employed. It is found that VLES results the most realistic reproduction of the observations. Furthermore, the non-hydrostatic model is improved by introducing laterally average terms, so the model can simulate the constrictions not only in the z-direction but also in the y-direction. Observational data from the Bosphorus Strait is employed to test the spatially average 2D non-hydrostatic model (SAM) in a realistic application. The simulations from SAM with a simple Smagorinsky type closure appear to be excessively diffusive and noisy. We show that SAM can benefit significantly from VLES turbulence closures. Second, the performance of different second-order turbulence closures is extensively tested in a hydrostatic model. Four different two-equation turbulence closures (k-&epsilon, k-&omega, Mellor-Yamada 2.5 (MY2.5) and a modified version of k- &epsilon) and K-Profile Parameterization (KPP) are selected for the comparison of 3D numerical simulations of the Red Sea overflow. All two-equation turbulence models are able to capture the vertical structure of the Red Sea overflow consisting of the BL and IL. MY2.5 with Galperin stability functions produce the largest salinity deviations from the observations along two sections across the overflow and the modified k-&epsilon exhibits the smallest deviations. The rest of the closures fall in between, showing deviations similar to one another. Four different closures (k- &epsilon, k-&omega, MY2.5KC and KPP) are also employed to simulate the Mediterranean outflow. The numerical results are compared with observational data obtained in the 1988 Gulf of Cadiz Expedition. The simulations with two-equation closures reproduce the observed properties of the overflow quite well, especially the evolution of temperature and salinity profiles. The vertically integrated turbulent salt flux displays that the overflow goes under significant mixing outside the west edge of the Strait of Gibraltar. The volume transport and water properties of the outflow are modified significantly in the first 50 km after the overflow exits the strait. The k-&epsilon and k-&omega cases show the best agreement with the observations. Finally, the interaction between the Red Sea overflow and Gulf of Aden (GOA) eddies has been investigated. It is found that the overflow is mainly transported by the undercurrent at the west side of the gulf. The transport of the overflow is episodic depending strength and location of GOA eddies. The most crucial finding is that the Red Sea overflow leaves the Gulf of Aden in patches rather than one steady current. Multiple GOA eddies induce lateral stirring, thus diapycnal mixing of the Red Sea outflow.

No description available.

The generation and evolution of internal solitary waves by intrusive gravity currents and river plumes are examined in an axisymmetric geometry by way of theory, experiments and numerical simulations. Full depth lock-release experiments and simulations demonstrate that vertically symmetric intrusions propagating into a two-layer fluid with an interface of finite thickness can launch a mode-2 double humped solitary wave. The wave then surrounds the intrusion head and carries it outwards at a constant speed. The properties of the wave's speed and shape are shown to agree well with a Korteweg-de Vries theory that is derived heuristically on the basis of energy conservation. The numerical code is also adapted to oceanographic scales in an attempt to simulate the interaction between the ocean and a river plume emanating from the mouth of the Columbia River. Despite several approximations, the fundamental dynamics of the wave generation process are captured by the model.

<div>A strongly implicit, nonlinear Crank-Nicolson-based finite-difference scheme was constructed for the numerical study of the self-similar behavior of viscous gravity currents. Viscous gravity currents are low Reynolds number flow phenomena in which a dense, viscous fluid displaces a lighter (usually immiscible) fluid. Under the lubrication approximation, the mathematical description of the spreading of these fluids is reduced to solving a nonlinear parabolic partial differential equation for the shape of the fluid interface. This thesis focuses on the finite-speed propagation of a power-law non-Newtonian current in a variable width channel-like geometry (a "Hele-Shaw cell'') subject to a given mass conservation/balance constraint. The proposed numerical scheme was implemented on a uniform but staggered grid. It is shown to be strongly stable, while possessing formal truncation error that is of second-order in space and it time. The accuracy of the scheme was verified by benchmarking it against established analytical solutions, which were obtained via a first-kind self-similarity transformation. A series of numerical simulations confirmed that the proposed scheme accurately respects the mass conservation/balance constraint. Next, the numerical scheme was used to study the second-kind self-similar behaviour of Newtonian viscous gravity currents flowing towards the end of a converging channel. Second-kind self-similar transformations are not fully specified without further information from simulation or experiment. Thus, using the proposed numerical scheme, the self-similar spreading and leveling leveling of the current was definitively addressed. The numerical results showed favorable comparison with experimental data.</div>

The first part of this thesis investigates the mixing of ambient fluid into axisymmetric high Reynolds number gravity currents. A series of laboratory experiments were conducted in which small scale gravity currents travelled along a wedge shaped channel with an increasing width in the downstream direction. The channel was filled with fresh water and the current was generated using saline solution introduced either by a rapid release of a known finite volume from behind a lock gate or by pumping at a constant rate into the apex of the channel. The distribution and evolution of the density of the flow with distance downstream was measured using a light attenuation technique. Additional experiments were performed by injecting parcels of dye in different regions of the flow in order to visualise the motion of fluid in and surrounding the gravity current. Unlike currents introduced by the release of a finite volume of fluid, where most mixing occurs in the head of the flow, currents produced from a steady source develop a steady tail region behind the front which is also found to entrain a significant amount of ambient fluid. In both types of current, we estimate the fraction of displaced ambient fluid that is entrained into the flow. We then derive a new class of self-similar solutions for gravity currents produced from a finite volume release of fluid. The second part of this thesis develops the experimental method of measuring mixing using light attenuation to investigate the mixing of liquid in a vertical conduit which results from a continuous stream of high Reynolds number gas bubbles. The experiments identify that the mixing in the wake of the bubbles leads to a net dispersive transport along the conduit. The process provides an explanation for the heat transfer within a volcanic conduit in the case of a gas-slug flow regime as occurs in the near surface region of volcanic conduits connected to surface lava lakes. We derive a theoretical model to estimate the heat flux associated with such a system using the empirical law for the dispersive mixing. The predicted heat flux associated with the bubbles is found to be comparable to the heat loss at the surface of lava lakes associated with radiative and convective heat loss. Given values for the gas flux, the lake area and the temperature at the surface of the lake, the model enables new predictions for the size of the volcanic conduit.

Hypoxia is frequently detected during summer in Corpus Christi Bay, Texas, and causes significant harm to benthic organism population and diversity. Hypoxia is associated with the density stratification in the Bay but the cause of stratification is uncertain. To support the study of hypoxia and stratification, a cyberinfrastructure based on the CUAHSI (Consortium of Universities for the Advancement of Hydrologic Science, Inc) Hydrologic Information System (HIS) is implemented. HIS unites the sensor networks in the Bay by providing a standard data language and protocol for transferring data. Thus hypoxia-related data from multiple sources can be compiled into a structured database. In Corpus Christi Bay, salinity data collected from many locations and times are synthesized into a three-dimensional space-time continuum using geostatistical methods. The three dimensions are the depth, the distance along a transect line, and time. The kriged salinity concentration in space and time illuminates the pattern of movement of a saline gravity current along the bottom of the Bay. The travel time of a gravity current in the Bay is estimated to be on the order of one week and the speed is on the order of 1 km per day. Statistical study of high-resolution wind data shows that the stratification pattern in the Bay is related to the occurrence of strong, southeasterly winds in the 5 days prior to the observation. This relationship supports the hypothesis that stratification is caused by the wind initiating hypersaline gravity currents which flow from Laguna Madre into Corpus Christi Bay. An empirical physical hypoxia model is created that tracks the fate and transport of the gravity currents. The model uses wind and water quality data from real-time sensors published by HIS to predict the extent and duration of hypoxic regions in the Bay. Comparison of model results with historical data from 2005 to 2008 shows that wind-driven gravity currents can explain the spatially heterogeneous patterns of hypoxic zones in Corpus Christi Bay. / text

Turbidity currents are one of the primary means of transport of sediment in the ocean. They are fast-moving, destructive fluid flows which are able to entrain sediment from the seabed and accelerate downslope in a process known as `ignition'. In this thesis, we investigate one particular model for turbidity currents; the `Parker model' of Parker, Pantin and Fukushima (1986), which models the current as a continuous sediment stream and consists of four equations for the depth, velocity, sediment concentration and turbulent kinetic energy of the flow. We propose two reduced forms of the model; a one-equation velocity model and a two-equation shallow-water model. Both these models give an insight into the dynamics of a turbidity current propagating downstream and we find the slope profile to be particularly influential. Regions of supercritical and subcritical flow are identified and the model is solved through a combination of asymptotic approximations and numerical solutions. We next consider the dynamics of the four-equation model, which provides a particular focus on Parker's turbulent kinetic energy equation. This equation is found to fail catastrophically and predict complex-valued solutions when the sediment-induced stratification of the current becomes large. We propose a new `transition' model for turbulent kinetic energy which features a switch from an erosional, turbulent regime to a depositional, stably stratified regime. Finally, the transition model is solved for a series of case studies and a numerical parameter study is conducted in an attempt to answer the question `when does a turbidity current become extinct?'.

[pt] A combinação de modelos numéricos com modelos computacionais tem contribuido muito para o melhor entendimento matemático de fluxos gravitacionais, porém esses modelos não podem substituir a análise através de trabalhos experimentais. O uso de modelos físicos em escala provou ser essencial na validação de equações para modelagem de correntes de turbidez. Com o objetivo de diminuir o nível de dificuldade em modelar numericamente essas correntes e de gerar modelos computacionais de alto desempenho, algumas simplificações foram feitas durante o desenvolvimento das equações de velocidade. Dessa forma, para provar que tais simplificações não iriam alterar os resultados numéricos do modelo, foram realizados inúmeros experimentos, coletando informações sobre a evolução espaço- temporal de velocidades das correntes de turbidez não- confinadas com e sem partículas. Comparando os resultados do modelo numérico com os do modelo físico, foi concluído que, infelizmente, as aproximações influenciaram os resultados. Contudo, os dados e a comparação visual entre as simulações também revelaram alguns resultados encorajadores, os quais estimularão pesquisas futuras para se melhorar a precisão da equação de velocidade utilizada no modelo numérico. / [en] The combination between numerical and computer models has improved dramatically the mathematical understanding of gravity currents; however, these models can not replace the analysis by experimental work. The use of scaled analogue models, or physical models, proved to be essential in validating velocity equations for turbidity currents. In order to reduce the level of difficulty to model mathematically these currents, some approximations were applied during the development of the velocity equation. Therefore, willing to prove that these approximations would not compromise the numerical results, innumerous experiments were performed to acquire a spatio-temporal velocity evolution database for both unconfined particle free and particulate turbidity flows. Comparing the results from the numerical and physical simulations, it was concluded that, unfortunately, the approximations have influenced the numerical results. Nevertheless, the data and visual comparisons between the simulations also revealed some encouraging results, which will stimulate some future research to improve the accuracy of the depth-averaging velocity equation.