A particle tracking velocimetry (PTV) system is used to investigate the turbulent properties at the free surface of shallow shear flows and a shallow vortex street (VS) wake flow. The resolution of the PTV system enables information to be gathered regarding the large-scale turbulent structure of these flows, and also enables analysis to proceed in both the temporal and spatial domains. Statistical tools such as the probability density function (PDF), autocorrelation and power spectral density (PSD) are utilised to characterise the turbulent properties at the flow surface. Two supercritical flows and one subcritical shallow shear flow are analysed. Taylor's frozen turbulence hypothesis is shown to be valid for these flows, and the integral length scales indicate that 2D isotropic structures with scales larger than the flow depth are present at the free surface. Such large-scale structures at the free surface are consistent with observations from dye visualisation experiments and with "spiral eddies" identified by Kumar, et al (1998). The longitudinal extent of near and intermediate wake fields for the shallow VS wake flow is well defined by the integral wake length scale specified by v.Carmer (2005). The near wake region is characterised by high rates of exchange between the mean flow and large-scale 2D coherent structures (2DCS). In the intermediate field, the rate of decay of the turbulent stress components greatly diminishes as the 2DCS are stabilised and dissipated under the action of bed friction. Multiple peaks are observed in the power spectral density of the turbulent fluctuations. The periodic shedding of 2DCS behind the circular cylinder is characterised by an energy peak at a Strouhal number of 0.21, and further energy peaks are observed in the near-wake region. The PSD estimates are consistent with the findings of v.Carmer (2005) in which a -5/3 decay law to high frequencies is observed, and no evidence of an inverse energy cascade is present.

The study of quasi-two-dimensional turbulent jets is relevant to chemical reactors, the coking process in oil refinement, as well as rivers flowing into lakes or oceans. In the event of a spillage of pollutants into a river, it is critical to understand how these agents disperse with the flow in order to assess damage to the environment. For such flows, characteristic streamwise and cross-stream dimensions can be much larger than the fluid-layer thickness, and so the flow develops in a confined environment. When the distance away from the discharge location is larger than ten times the fluid-layer thickness, the flow is referred to as a quasi-two-dimensional jet. From experimental observations using dyed jets and particle image velocimetry, we find that the structure of a quasi-two-dimensional jet consists of a high-speed meandering core with large counter-rotating eddies developing on alternate sides of the core. The core and eddy structure is self-similar with distance from the discharge location. The Gaussianity of the cross-stream distribution of the time-averaged velocity is due, in part, to the sinuous instability of the core. To understand the transport and dispersion properties of quasi-two-dimensional jets we use a time-dependent advection--diffusion equation, with a mixing length hypothesis accounting for the turbulent eddy diffusivity. The model is supported by experimental releases of dye in jets or numerical releases of virtual passive tracers in experimentally-measured jet velocity fields. We consider the statistical properties of this flow by releasing and then tracking large clusters of virtual particles in the jet velocity field. The probability distributions of two-point properties (such as the distance between two particles) reveal large streamwise dispersion. Owing to this streamwise dispersive effect, a significant amount of tracers can be transported faster than the speed predicted by a simple advection model. Using potential theory, we determine the flow induced by a quasi-two-dimensional jet confined in a rectangular domain. The streamlines of the induced flow predicted by the theory agree with experimental measurements away from the jet boundary. Finally, we investigate the case of a quasi-two-dimensional particle-laden jet. Depending on the bulk concentration of dense particles, we identify different flow regimes. At low concentrations, the jet features the same core and eddy structure observed without the particles, and thus quasi-two-dimensional jet theory can apply to some extent. At larger concentrations, we observe an oscillating instability of the particle-laden jet.

A novel acoustic sensor has been developed, capable of remotely monitoring the free surface ‘fingerprint’ of shallow flows. Temporal and spatial properties of this pattern are shown to contain information regarding the nature of the flow itself. The remote measurement can thereby be used to infer the bulk flow properties such as depth, velocity, and the hydraulic roughness of the pipe. The instrument is non-invasive and is also low cost, low maintenance, and low power. Such a device will allow for widespread monitoring of flow conditions in drainage networks, enabling pro-active maintenance and reliable real-time control.

This thesis concerns the occurrence of the large-scale bed and plan forms known as alternate bars and meandering, and the internal structures of the flow associated with their formation. The work is to be viewed as an extension of previous work by da Silva (1991), Yalin (1992), and Yalin and da Silva (2001). As a first step in this work, the criteria for occurrence of alternate bars and meandering of Yalin and da Silva (2001) is re-considered in view of additional field and laboratory data from the recent literature and data resulting from two series of experimental runs carried out in two sediment transport flumes. This leads to a number of modifications of the boundary-lines in the related existence-region diagram of Yalin and da Silva. The size of the largest horizontal coherent structures (HCS’s) of an alternate bar inducing flow was then investigated experimentally on the basis of three series of flow velocity measurements. These were carried out in a 21m-long, 1m-wide straight channel, conveying a 4cm-deep flow. The bed consisted of a silica sand having a grain size of 2mm; its surface was flat. The measurements were carried out using a Sontek 2D Micro ADV. The horizontal burst length was found to be between five and seven times the flow width. The effect of the HCS’s on the mean flow was also investigated. A slight internal meandering of the flow caused by the superimposition of burst-sequences on the mean flow was clearly detectable. Finally, with the aid of three new series of measurements in the same channel, an attempt was made to penetrate the dynamics and life-cycle of the HCS’s. For this purpose, quadrant analysis was used; the cross-sectional distribution of relevant statistical turbulence-related parameters was investigated; and cross-correlations of flow velocity along the flow depth and across the channel were performed. The analysis indicates that the HCS’s originate near the channel banks, with the location of ejections and sweeps being anti-symmetrically arranged with regard to the channel centreline, and then evolve so as to occupy the entire depth of the water and the entire width of the channel. / Thesis (Ph.D, Civil Engineering) -- Queen's University, 2010-03-09 10:20:53.596

A numerical solution algorithm based on finite volume method is developed for unsteady, two-dimensional, depth-averaged shallow water flow equations. The model is verified using test cases from the literature and free surface data obtained from measurements in a laboratory flume. Experiments are carried out in a horizontal, rectangular channel with vertical solid boxes attached on the sidewalls to obtain freesurface data set in flows where three-dimensionality is significant. Experimental data contain both subcritical and supercritical states. The shallow water equations are solved on a structured, rectangular grid system. Godunov type solution procedure evaluates the interface fluxes using an upwind method with an exact Riemann solver. The numerical solution reproduces analytical solutions for the test cases successfully. Comparison of the numerical results with the experimental two-dimensional free surface data is used to illustrate the limitations of the shallow water equations and improvements necessary for better simulation of such cases.

Shallow flows are those whose width is significantly larger than their depth. In these types of flows, two dimensional coherent structures can be generated and can influence the flow greatly by the lateral transfer of mass and momentum. The development of coherent structures as a result of flow instabilities has been a topic of interest for environmental fluid mechanics for decades. Studies on the use of linear modal stability analysis is commonly found in literature. However, the relatively recent development in the field of hydrodynamic stability suggests that the traditional linear modal stability analysis does not describe the behaviour of the perturbations in finite time. The discrepancy between asymptotic behaviour and finite time behaviour is particularly large in shear driven flows and it is most likely to be the case for shallow flows. This study aims to provide a better understanding of finite time growth of perturbation energy in shallow flows. The three cases of shallow flows evaluated are the mixing layer, jet and wake. The critical cases are obtained through the linear modal analysis and nonmodal analysis was conducted to show the transient behaviour in finite time for what is so-called marginally stable. Finally, the thesis concludes by generalizing the finite time energy growth in the S-k space.

Yes / A set of shallow-water equations (SWEs) based on a k-epsilon Reynold stress model is established to simulate the turbulent flows over a complex roughness bed. The fundamental equations are discretized by the second-order finite-difference method (FDM), in which spatial and temporal discretization are conducted by staggered-grid and leap-frog schemes, respectively. The turbulent model in this study stems from the standard k-epsilon model, but is enhanced by replacing the conventional vertical production with a more rigorous and precise generation derived from the energy spectrum and turbulence scales. To verify its effectiveness, the model is applied to compute the turbulence in complex flow surroundings (including a rough bed) in an abrupt bend and in a natural waterway. The comparison of the model results against experimental data and other numerical results shows the robustness and accuracy of the present model in describing hydrodynamic characteristics, especially turbulence features on the complex roughness bottom. / National Key Research and Development Program of China (Grant No: 2016YFE0122500, 2013CB036401 and 2013CB036402), China Postdoctoral Science Foundation (Grant No: 2016M591184) and Programme of Introducing Talents of Discipline to Universities (Grant No: BC2018038) / Research Development Fund Publication Prize Award winner, June 2019.

Yes / Understanding the dynamic free surface of geophysical flows has the potential to enable direct inference of the flow properties based on measurements of the free surface. An important step is to understand the inherent response of free surfaces in depth-limited flows. Here a model is presented to demonstrate that free surface oscillatory spatial correlation patterns result from individual surface features oscillating vertically as they advect over space and time. Comparison with laboratory observations shows that these oscillating surface features can be unambiguously explained by simple harmonic motion, whereby the oscillation frequency is controlled by the root-mean-square water surface fluctuation, and to a lesser extent the surface tension. This demonstrates that the observed “complex” wave pattern can be simply described as an ensemble of spatially and temporally distributed oscillons. Similarities between the oscillon frequency and estimated frequency of near-bed bursting events suggest that oscillon behaviour is linked with the creation of coherent flow structures.

Laboratory experiments were conducted to investigate the effect of low relative depth and high Froude number on the dimensionless critical shear stress (Shields parameter). Spherical particles of four different densities and an 8mm diameter were used as movable test material. The relative depth ranged from 2 to 12 and the Froude number ranged from 0.36 to 1.29. The results show that the traditional Shields diagram cannot be used to predict the incipient motion of coarse sediment particles when the relative depth is below 10 and the Froude number is above 0.5, approximately. Experiments using glass balls, whose density is almost identical to that of natural gravel, show that the Shields parameter can be twice as large in shallow flows than in deep flows. The results also show that the Shields parameter is dependent on the density of the particles. Data obtained from other studies support the findings of the present work. These findings can result in significant cost savings for riprap. Additionally, velocity profiles using a laser-Doppler velocimeter (LDV) were taken for the glass ball incipient motion experiments. The purpose of this was to study possible changes in the velocity distribution with decreasing relative depth and increasing Froude number. The results show that the von Karman and integral constants in the law of the wall do not change in the range of relative depths and Froude numbers tested. / Master of Science

Dans ce projet de recherche, on s'intéresse au développement et à l'évaluation de nouvelles méthodes numériques pour les écoulements peu profonds. De nouvelles techniques de discrétisation spatiales et temporelles des équations sont proposées. La première partie de la thèse est dédiée au développement d'une méthode des volumes finis explicite d'ordre élevé et d'une famille de schémas semi-implicites qui sont efficaces pour la modélisation des processus lents et rapides dans les écoulements océaniques et atmosphériques. La deuxième partie du projet de recherche concerne la construction d'un schéma numérique efficace sans solveur de Riemann pour les écoulements peu profonds avec une topographie variable sur un maillage non structuré. Dans cette partie de la thèse, une nouvelle approche est proposée pour l'analyse de stabilité des schémas numériques non structurés pour les équations en eaux peu profondes. Dans la troisième partie de la thèse, deux schémas de volumes finis sont développés pour les lois de conservation sur des surfaces courbes qui ont un large potentiel d'être appliqués aux écoulements peu profonds sur la sphère. Dans ces cas, les schémas numériques sont développés en adoptant la démarche suivie par Stanley Osher. Cette démarche consiste à utiliser des systèmes hyperboliques simples qui génèrent des phénomènes d'ondes complexes et des solutions qui ont différentes structures. Ces solutions sont très efficaces pour tester les méthodes numériques. Dans notre cas, nous avons utilisé les équations de Burgers qui ont joué un rôle très important dans le développement des schémas numériques à capture de chocs en mécanique des fluides. / This research project focuses on the development and evaluation of numerical methods for shallow flows by proposing new spatial and temporal discretization techniques. First, a new high-order explicit finite volume method and a class of semi-implicit schemes are introduced which are effective for modelling fast and slow waves in oceanic and atmospheric flows. In the second part of the research project, a central-upwind scheme is proposed for shallow water flows on variable topography using unstructured grids. In this part of the project, a new approach is proposed for the stability analysis of unstructured numerical schemes for shallow water equations. In the third part of the thesis, two finite volume methods are developed for the conservation laws on curved geometries which are potentially applicable to shallow flows on a sphere. For such cases, numerical schemes are developed by using the approach followed by Stanley Osher. This approach employs simple hyperbolic systems which generate complex wave phenomena, and solutions that are effective for assessing numerical methods. In our case, Burgers’ equations are used since they have played an important role in the development of shock-capturing schemes in fluid mechanics.