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A numerical model is presented of vertically homogeneous shallow flows with variable horizontal density. The governing equations represent mass and momentum conservation of a liquid-species mixture, and mass conservation of the species within a control volume. Here, the term species refers to material transported with the liquid flow. For example, when the species is taken to be suspended sediment, the model provides an idealised simulation of hyper-concentrated sediment-laden flows. The volumetric species concentration acts as an active scalar, allowing the species dynamics to influence the flow structure. The model can simulate flows driven by depth and density differences in the horizontal. The governing equations are written in a deviatoric, hyperbolic form to facilitate their solution by means of a Godunov-type finite volume scheme appropriate for flows containing sharp fronts. The deviatoric governing equations ensure that flux gradient and source terms are balanced (and there is no need for further numerical balancing). The numerical model is first verified for constant density cases, for which the governing equations reduce to the conventional coupled shallow water and species transport equations. Close agreement between numerical predictions and benchmark test solutions illustrate the model's ability to capture rapidly-varying flow features over uniform and non-uniform bathymetries. For variable-density cases, analytical steady-state solutions are derived for two simple cases, one with uniform bathymetry and the other with sinusoidal bathymetry. Detailed parameter studies are then undertaken to examine the effects of varying the initial density and depth in different regions. The shock-capturing scheme resolves all sharp features in the flow such as bore, shear waves, shock diamond like features, contact discontinuities and locally intense vortices. These interesting and novel nonlinear features are unique to variable density flows. The validated numerical model is applied to an idealised case of a hyperconcentrated sediment-laden debris-type flow along a tributary entering a river. The predicted evolution of the free surface flow field is qualitatively similar to observations of an actual debris flows into a river connected to the Upper Yangtze.

The convenience of Operational Modal Analysis (OMA), over conventional Experimental Modal Analysis (EMA), has seen to its increasing popularity over the last decade for the purpose of evaluating dynamic properties of structures. OMA features an advantage of requiring only output information, which is in tandem with its main drawback of lacking scaled modeshape information. While correctly scaled modeshapes can be assumed under a restrictive assumption of spectrally white inputs, in reality, input spectra are at best broadband in nature. In this thesis, an OMA method for Multiple-Input Multiple-Output (MIMO) applications in mechanical structures is developed. The aim is to separate MIMO responses into a collection of Single-Input Single-Output (SISO) processes (matrix FRF) using cepstral-based methods, under less restrictive and hence more realistic coloured broadband excitation. Existing cepstral curve-fitting techniques can be subsequently applied to give regenerated FRFs with correct relative scaling. This cepstral-based method is based on the matrix Mean Differential Cepstrum (MDC) and operates in the frequency domain. Application of the matrix MDC onto MIMO responses leads to a matrix differential equation which together with the use of finite differences, directly solves or identifies the matrix FRF in a propagative manner. An alternative approach based on whitened MIMO responses can be similarly formulated for the indirect solution of the matrix FRF. Both the direct and indirect approaches can be modified with a Taylor series approximation to give a total of four propagative solution sequences. The method is developed using relatively simple simulated and experimental systems, involving both impulsive and burst random excitations. Detailed analysis of the results is performed using more complicated Single-Input Multiple-Output (SIMO) and MIMO systems, involving both driving and non-driving point measurements. The use of the matrix MDC method together with existing cepstral curve-fitting technique to give correct relative scaling is demonstrated on a simulated MIMO system with coloured inputs. Accurate representation of the actual FRFs is achieved by the matrix MDC technique for SIMO set-ups. In MIMO scenarios, excellent identification was obtained for the case of simulated impulsive input while the experimental and burst random input cases were less favourable. The results show that the matrix MDC technique works in MIMO scenarios, but possible noise-related issues need to be addressed in both experimental and burst random input cases for a more satisfactory identification outcome.

M.Ing. / The aim of this dissertation is to apply numerical aerodynamic principles to the characterization of an alternative stepped aerofoil concept. The accurate and efficient determination of the aerodynamic forces caused by the relative fluid motion and the consequent lift and drag coefficients are essential for the characterization of new aerofoils. The numerical method used is in the form of a Computational Fluid Dynamics code, which integrates the Navier-Stokes equations through finite-volume dictretization principals. A two-dimensional approximate analysis procedure is used together with a two-equation turbulence approximation in the form of the "standard" k-c turbulence model. Available software is used and adapted where applicable. A suitable method for comparing wing section characteristics as a function of profile geometry and attitude is developed in this thesis. This is achieved by first refining a numerical test case and quantifying the influences of model parameters such as grid design, boundary conditions and solution variables. Alternative geometrical aerofoil concepts can then be characterized by employing the same principles. This thesis contains selected results of hundreds such numerical simulations, all of which were necessary to refine the test case and eventually characterize the aerofoils. The proposed wing section geometry, incorporating a rearward-facing step shows some improvement in aerodynamic performance over a standard reference case. Geometrical variations of the step concept are also investigated and can later be used in an optimization procedure. A transient simulation approach is employed for unsteady cases and flow visualization is done in order to learn more about the unique aerodynamic action of the proposed concept. Experimental results obtained in a wind tunnel for the pressure around the investigated aerofoils are used to verify numerical results. Further development in the numerical approach may include the use of additional, more advanced turbulence models. This may allow the research of more complex phenomena such as stall and also broader ranges of Reynolds numbers in more detail. To complete the characterization process, the moment coefficients should also be included.

The Fraser River plume is the brackish surface layer formed when the Fraser River discharges into the Strait of Georgia. Two approaches to understanding the dynamics of the plume are discussed. Initially, a series of field observations was carried out in the plume. These consisted mainly of CSTD profiles and current profiles in the upper 10-20 meters of the water column. Also, a surface current meter was installed for 34 days at the mouth of the Fraser River. The principal conclusions of the field observations are: the plume is strongly sheared in the vertical and strongly stratified; this vertical structure is most apparent in the vicinity of the river mouth, and around the time of maximum river discharge (near low water in the Strait); and that the water moving outward from the river mouth subsequently acquires velocities and salinities appropriate to the water beneath it with length and time scales for this change of order 50 km and 8 hours. The plume thickness varies between 0 and 10 meters; the salinity varies from 0 to that of the water beneath it (approx. 25 ‰); and the difference between the plume velocity and that of the water beneath it varies from up to 3.5 m/sec to 0 m/sec, and is typically of order 0.5 m/sec over much of the plume area. Inspired by the field data, a model of the thin upper layer was developed. The independent variables are the two components of transport in the upper layer, the thickness of the layer, and the integrated salinity in the upper layer. The bottom of the upper layer has been tentatively defined by an isopycnal surface. The mixing across this interface is modelled by an upward flux of salt water (entrainment), and a downward flux of brackish water (termed depletion in this work). The dynamical effects included in this model are: the local time derivative; the field accelerations; the buoyant spreading pressure gradient (including the effects of salinity on the density field); the entrainment of tidally moving water and the loss by the depletion mechanism of water with the plume momentum; the frictional stress between the plume and the water beneath it; the forcing due to the baroclinic tidal slopes; and the Coriolis force. Subsets of the full model equations are examined, to clarify certain aspects of the plume dynamics. Preliminary results from the numerical solution of the full model eguations are presented, and a comparison is made between the paths of lagrangian trackers produced by the model and drogue tracks observed in the plume. Future improvements to the model are discussed. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

Mathematical modeling is a powerful tool to study and analyze the disease dynamics prevalent in the community. This thesis studies the dynamics of two time since infection structured vector borne models with direct transmission. We have included disease induced death rate in the first model to form the second model. The aim of this thesis is to analyze whether these two models have same or different disease dynamics. An explicit expression for the reproduction number denoted by R0 is derived. Dynamical analysis reveals the forward bifurcation in the first model. That is when the threshold value R0 < 1, disease free-equilibrium is stable locally implying that if there is small perturbation of the system, then after some time, the system will return to the disease free equilibrium. When R0 > 1 the unique endemic equilibrium is locally asymptotically stable. For the second model, analysis of the existence and stability of equilibria reveals the existence of backward bifurcation i.e. where the disease free equilibrium coexists with the endemic equilibrium when the reproduction number R02 is less than unity. This aspect shows that in order to control vector borne disease, it is not sufficient to have reproduction number less than unity although necessary. Thus, the infection can persist in the population even if the reproduction number is less than unity. Numerical simulation is presented to see the bifurcation behaviour in the model. By taking the reproduction number as the bifurcation parameter, we find the system undergoes backward bifurcation at R02 = 1. Thus, the model has backward bifurcation and have two positive endemic equilibrium when R02 < 1 and unique positive endemic equilibrium whenever R02 > 1. Stability analysis shows that disease free equilibrium is locally asymptotically stable when R02 < 1 and unstable when R02 > 1. When R02 < 1, lower endemic equilibrium in backward bifurcation is locally unstable. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2020. / FAU Electronic Theses and Dissertations Collection