Predicting the evolution of turbulent gravity currents is of great interest in many areas of geophysics and engineering, in particular due to their impact on the environment. In most practical applications in river, coastal and ocean engineering, gravity currents propagate over loose surfaces containing large scale bedforms (e.g., dunes). In others, arrays of obstacles (e.g., ribs) are often used as protective measures on hilly terrains to stop or slow down gravity currents in the form of powder-snow avalanches. To predict the capacity of a turbulent gravity current propagating over a loose bed to entrain, carry, and deposit sediment requires a detailed understanding of its structure and the role played by the large-scale instabilities present in the flow. The present study uses high-resolution Large Eddy Simulation to study the physics of high Reynolds number compositional Boussinesq gravity currents with large and small volume of release in lock-exchange configurations and their dynamic effects on various obstacles (e.g., bedforms, flow retarding obstacles, submerged dams that are used to control sediment deposition in reservoirs). The study shows that gravity currents propagating over large-scale roughness elements reach a turbulent drag-dominated regime in which the front velocity decays proportional to t-1/2, similar to the case of gravity currents propagating within a porous medium. Though the establishment of a regime in which the flow evolution is mainly determined by the balance between the turbulent drag and the buoyancy force driving the flow was expected, the fact that the law of decay of the front velocity with time is identical for gravity currents propagating over roughness elements and in a porous medium of uniform porosity is not obvious. The simulations provide detailed information on the temporal evolutions of the front velocity, energy balance, sediment entrainment capacity and the flow instabilities, and of the distributions of the density, velocity, local dissipation rate and bed shear stresses at different stages of the propagation of the gravity current. The study investigates of the effect of the shape and relative size of the obstacles, with respect to the current height, on the structure of the current and on the differences with the simpler, but much more widely studied case of a gravity current propagating over a flat smooth surface. For example, the simulation results are used to explain why gravity currents propagating over dunes have a much larger capacity to entrain sediment than gravity currents propagating over ribs of the same height and with similar spacing. The accurate estimation of impact of gravity current on the structures over its path is very important from engineering point of view since many submerged cables over the ocean bottom or submerged dams in reservoirs are under the risk of such impacts. The simulations of gravity currents propagating past arrays of ribs or isolated dams are used to estimate the characteristic times and magnitudes of the hydrodynamic impact forces on these obstacles. This information is crucial for the proper design of these structures. The study shows the critical role played by flow disturbances (e.g., backward propagating hydraulic jumps) that form as a result of the interaction between the current and the large-scale obstacles. Finally, the study investigates scale effects between the Reynolds numbers at which most experimental investigations of gravity currents are conducted and Reynolds numbers at field scale.

Corpus Christi Bay in Texas is a wind driven system, and under most conditions winds over the bay mix the water column vertically. However, seasonal, episodic, bottom-water hypoxia has been observed in the bay in conjunction with vertical salinity stratification. This stratification may be caused by dense gravity currents entering the bay. Understanding and modeling the mechanisms that result in stratification in Corpus Christi Bay may help predict hypoxia, and for this reason that is the focus of this dissertation. An evaluation of existing gravity current modeling techniques shows that most currently available models are designed to capture either phenomena local to a gravity current, such as gravity current entrainment and spreading, or larger scale phenomena such as wind mixing and large-scale circulation, but not both. Because gravity current mixing in Corpus Christi Bay is enhanced by wind-induced turbulence, both local gravity current physics and wind mixing effects are critical elements governing gravity current propagation in Corpus Christi Bay. As existing models do not represent gravity current entrainment and wind mixing together, this dissertation develops a coupled model system that accounts explicitly for turbulent wind mixing of a bottom-boundary layer, in addition to representing other local features of dense gravity current propagation such as entrainment and spreading. The coupled model system consists of a 2D depth-averaged hydrodynamic model that calculates gravity current mixing and spreading, coupled with a 3D hydrodynamic model whose domain includes a lighter ambient fluid surrounding the gravity current. The coupled models have flexible boundary conditions that allow fluid exchange to represent mixing from both gravity current entrainment and wind mixing. The coupled model system’s development, verification and application in Corpus Christi Bay advances understanding of gravity current mechanisms, and contributes to our scientific understanding of hypoxia in Corpus Christi Bay. This modeling technique has the flexibility to be applied to other density-stratified systems that are shallow and potentially wind-driven, such as shallow desalination brine disposal sites. / text

yes / The accurate prediction of the dilution and motion of the produced denser water (e.g. discharge of concentrated brine generated during solution mining and desalination) is of importance for environmental protection. Boundary conditions and ambient stratification can significantly affect the dilution and motion of gravity currents. In this study, a multiphase model is applied to simulate the gravity current descending a slope into a linearly stratified ambient. The k- turbulence model is used to better simulate the near bed motion. The mathematical model, initial and boundary conditions and the details of the numerical scheme are described. The time-dependent evolution of the gravity current, the flow thickness and the velocity and density field are simulated for a range of flow parameters. Simulations show that the Kelvin–Helmholtz billows are generated at the top of trailing fluid by the interfacial velocity shear. The K-H type instability becomes weaker with the slope distance from the source due to the decrease of the interfacial velocity shear along slope. The ambient stratification restricts and decreases the current head velocity as it descends slope, which differs from the situation in homogenous ambient while the head velocity remains an approximately steady state. Motion of the descending flow into the stratified ambient has two stages: initial acceleration and deceleration at later stage based on the balance of inertial, buoyancy and friction forces. When the descending current approaches the initial neutral position at later stage, it separates from the slope and spreads horizontally into environment. The simulated results, such as vertical velocity and density profiles and front positions, agree well with the measurements, indicating that the mathematical model can be successfully applied to simulate the effect of the boundary condition and ambient stratification on the dilution and propagation of gravity currents. / UK EPSRC

An analytical and experimental study of boundary gravity currents propagating through a two-layer stratified ambient of finite vertical extent is presented. The theoretical discussion considers slumping, supercritical gravity currents, i.e. those that generate an interfacial disturbance whose speed of propagation matches the front speed, U and follows from the classical analysis of Benjamin [J. Fluid Mech. 31, pp. 209-248, 1968]. In contrast to previous investigations, the amplitude of the interfacial disturbance is parameterized so that it can be determined straightforwardly from ambient layer depths. The theoretical model, which is applicable to the special case where the depth, D, of the gravity current fluid at the initial instant spans the channel depth, H, shows good agreement with experimental measurements and also analogue numerical simulations performed in conjunction with the present investigation. Unfortunately, it is difficult to extend our theoretical results to the more general case where D < H. Reasons for this difficulty will be discussed. From experimental and numerical observations, the interface thickness is observed to negligibly affect the speed of supercritical gravity currents even in the limit where the interface spans the channel depth so that the ambient fluid is linearly stratified over the whole of its depth. Conversely, subcritical gravity currents show a mild upward trend of U on the interface thickness. Finally, the effects of densities, ambient depths, interface thickness and D on the horizontal position, X where deceleration first begins are considered. In contrast to the uniform ambient configuration, the gravity current can propagate without decelerating beyond 12 lock lengths and decelerate as early as 1 lock length. / Thermo Fluids

No description available.

Materials can flow down a slope in a wide range of geophysical and industrial contexts, including lava flows on volcanoes and thin films on coated surfaces. The aim of my research is to provide quantitative insight into these forms of motion and their dependence on effects of the topography, the volume and the rheology of the flowing structure. Numerous different problems are investigated through mathematical models, which are developed analytically and confirmed by laboratory experiments. The initial advance of long lava flows is studied by considering the flow of viscous fluid released on sloping channels. A scaling analysis, in agreement with analog experiments and field data, offers a practical tool for predicting the advance of lava flows and conducting hazard analysis. A simple and powerful theory predicts the structure of flows resulting from any time-dependent release of fluid down a slope. Results obtained by the method of characteristics reveal how the speed of the advancing front depends importantly on the rate of fluid supplied at an earlier time. Viscous flows on surfaces with different shapes are described by similarity solutions to address problems motivated by engineering as well as geophysical applications. Pouring viscous fluid out of a container can be a frustratingly slow process depending on the shape and the degree of tipping of the container. The discharge rate of the fluid is analysed in simple cases, shedding light on how containers can be emptied most quickly in cosmetic and food industries. In a separate study motivated by coating industries, thin films are shown to evolve with uniform thickness as they drain near the top of a horizontal cylinder or sphere. The leading edge eventually splits into rivulets as predicted theoretically and confirmed by experiments. Debris flows can develop levees and trigger avalanches which are studied by considering dense granular flows down a rough inclined plane. Granular materials released down a slope can produce a flowing structure confined by levees or trigger avalanches at regular intervals, depending on the steady rate of supply. The experimental results are discussed using theoretical ideas of shallow granular flows. Finally, materials flowing in long and slender ducts are investigated theoretically to better understand the digestive and urinary systems in biology. The materials are pumped in an elastic tube by translating waves of muscular contraction and relaxation. The deformation of the tube is predicted by solving a free-boundary problem, a similar mathematical exercise to predicting the moving boundaries of materials spreading on slopes.

Thesis (PhD (Civil Engineering))--Stellenbosch University, 2008. / The velocity, density and turbulence profiles of a horizontal, saline gravity current were measured experimentally. Stable stratfication damped the turbulence and prevented the gravity current from becoming self-similar. The velocity and density prfiles were measured simultaneously and non-intrusively with particle image velocimetry scalar (PIV-S) technology. The application of the PIV-S technology had to be extended in order to measure the continuously stratified gravity current. Measurement of the Reynolds fluxes and Reynolds stresses revealed the anisotropic turbulent transport of mass and momentum within the gravity current body. These measurements also allowed the interaction between turbulence and stratification to be studied. The measured profiles were used to evaluate the accuracy of a gravity current model which did not assume self-similarity. The gravity current model was based on a Reynolds-averaged Navier-Stokes (RANS) multispecies mixture model. The Reynolds flux and Reynolds stress profiles did not show self-similarity with increasing downstream distance. Comparison of the vertical and horizontal Reynolds fluxes showed that gravity strongly damped the vertical flux. At a downstream location, where the bulk Richardson number was supercritical, the shear production profile had a positive inner (near bed) peak and a positive outer peak, while the buoyancy production pro le had a negative outer peak. Further downstream, where the bulk Richardson number was near-critical, the outer shear and buoyancy production peaks disappeared, due to the continuous damping of the turbulence intensities by the stable stratification. However, near bed shearing allowed the inner shear production peak to remain. Sensitivity analyses of different turbulence models for the gravity current model showed that the standard k -e turbulence model, as well as the Renormalization Group theory (RNG) k -e turbulence model, generally underpredicted the mean streamwise velocity profile and overpredicted the excess density pro le. The flux-gradient hypothesis, used to provide closure for the Reynolds uxes, modelled the vertical Reynolds ux reasonably, but not the horizontal flux. This did not compromise the results, since the horizontal gravity current had the characteristics of a boundary-layer ow, where the horizontal flux does not contribute significantly to the flow structure. It was shown that the gravity current model, implementing the standard k -e turbulence model with a constant turbulent Schmidt number of ot = 1;3, produced profiles which were within 10% - 20% of the measured profiles.

In this thesis, we consider four different problems in membrane filtration, using a different mathematical approach in each instance. We account for the fluid-driven deformation of a filtercake using nonlinear poroelasticity in Chapter 2. By considering feeds with very high and very low particle concentrations, we introduce a quasi-static caking model that provides a suitable approximation to the full model for the physically realistic concentration regimes. We illustrate the agreements and differences between our model and the existing conventional cake-filtration law. In Chapter 3, we introduce a stochastic model for membrane filtration based on the quantised nature of the particles and show how it can be applied for feeds with different particle types and membranes with an interconnected pore structure. This allows us to understand the relation between the effects of clogging on the level of an individual pore and on the macroscopic level of the entire membrane. We conclude by explaining the transition between the discrete and continuous model based on the Fokker--Planck equation. In Chapter 4, we consider the inverse problem of determining the underlying filtration law from the spreading speed of a particle-laden gravity current. We first couple the theory of gravity currents with the stochastic model developed in Chapter~3 to determine a filtration law from a given set of experiments. We then generalise this idea for the porous medium equation, where we show that the position of the front follows a power law for the conventional filtration laws, which allows us to infer the clogging law in certain instances. We conclude the thesis by showing in Chapter 5 how we can combine experimental measurements for the clogging of a depth filter and simple fluid dynamics to accurately predict the pressure distribution in a multi-capsule depth filter during a filtration run.

Physical experiments are used to investigate the influence of the Coriolis forces on flow structures in channelized turbidity currents, and their implication for the evolution of straight and sinuous submarine channels. Initial tests were used to determine whether or not saline density currents are a good surrogate for particle-laden currents. Results imply that this assumption is valid when turbidity currents are weakly-depositional and have similar velocity and turbulence structures to saline density currents. Second, the controls of Coriolis forces on flow structures in straight channel sections are compared with two mathematical models: Ekman boundary layer dynamics and the theory of Komar [1969]. Ekman boundary layer dynamics prove to be a more suitable description of flow structures in rotating turbidity currents and should be used to derive flow parameters from submarine channels systems that are subjected to Coriolis forces. The significance of Coriolis forces for submarine channel systems were determined by evaluating the dimensionless Rossby number RoW. The Rossby number is defined as the ratio of the flow velocity, U, of a turbidity current to the channel width, W, and the rotation rate of the Earth represented by the Coriolis parameter, f. Coriolis forces are very significant for channel systems with RoW ≤ O(1). Third, the effect of Coriolis forces on the internal flow structure in sinuous submarine channels is considered. Since previous studies have only considered pressure gradient and centrifugal forces, the Coriolis force provides a crucial contribution to the lateral momentum balance in channel bends. In a curved channel, both the Rossby number RoW and the ratio of the channel curvature radius R to the channel width W, determine whether Coriolis forces affect the internal flow structure. The results demonstrate that Coriolis forces can cause a significant shift of the density interface and the downstream velocity core of channelized turbidity currents. The sediment transport regime in high-latitude channel systems, which have RoW << R/W, is therefore strongly influenced by Coriolis forces. Finally, these findings are incorporated into a conceptual model describing the evolution of submarine channels at different latitudes. For instance, the Northern Hemisphere channels have a distinctly higher right levee system and migrate predominantly to the left side and generally exhibit a low sinuosity. In contrast, low latitude channel systems have RoW >> R/W so that centrifugal forces are more dominant. This results in more sinuous submarine channel systems with varying levee asymmetries in subsequent channel bends. In conclusion, Coriolis forces are negligible around the equator but should be considered in high latitude systems, particularly when RoW ~ O(1) and RoW << R/W.

Physical experiments are used to investigate the influence of the Coriolis forces on flow structures in channelized turbidity currents, and their implication for the evolution of straight and sinuous submarine channels. Initial tests were used to determine whether or not saline density currents are a good surrogate for particle-laden currents. Results imply that this assumption is valid when turbidity currents are weakly-depositional and have similar velocity and turbulence structures to saline density currents. Second, the controls of Coriolis forces on flow structures in straight channel sections are compared with two mathematical models: Ekman boundary layer dynamics and the theory of Komar [1969]. Ekman boundary layer dynamics prove to be a more suitable description of flow structures in rotating turbidity currents and should be used to derive flow parameters from submarine channels systems that are subjected to Coriolis forces. The significance of Coriolis forces for submarine channel systems were determined by evaluating the dimensionless Rossby number RoW. The Rossby number is defined as the ratio of the flow velocity, U, of a turbidity current to the channel width, W, and the rotation rate of the Earth represented by the Coriolis parameter, f. Coriolis forces are very significant for channel systems with RoW ≤ O(1). Third, the effect of Coriolis forces on the internal flow structure in sinuous submarine channels is considered. Since previous studies have only considered pressure gradient and centrifugal forces, the Coriolis force provides a crucial contribution to the lateral momentum balance in channel bends. In a curved channel, both the Rossby number RoW and the ratio of the channel curvature radius R to the channel width W, determine whether Coriolis forces affect the internal flow structure. The results demonstrate that Coriolis forces can cause a significant shift of the density interface and the downstream velocity core of channelized turbidity currents. The sediment transport regime in high-latitude channel systems, which have RoW << R/W, is therefore strongly influenced by Coriolis forces. Finally, these findings are incorporated into a conceptual model describing the evolution of submarine channels at different latitudes. For instance, the Northern Hemisphere channels have a distinctly higher right levee system and migrate predominantly to the left side and generally exhibit a low sinuosity. In contrast, low latitude channel systems have RoW >> R/W so that centrifugal forces are more dominant. This results in more sinuous submarine channel systems with varying levee asymmetries in subsequent channel bends. In conclusion, Coriolis forces are negligible around the equator but should be considered in high latitude systems, particularly when RoW ~ O(1) and RoW << R/W.