Localised optimal initial perturbations are studied to gain an understanding of the global stability properties of streamwise corner-flow. A self-similar and a modified base-flow are considered. The latter mimics a characteristic deviation from the self-similar solution, commonly observed in experiment. Poweriterations in terms of subsequent direct and adjoint linearised Navier-Stokes solution sweeps are employed to converge optimal solutions for two optimisation times. The optimal response manifests as a wave packet that initially gains energy through the Orr mechanism and continues growing exponentially thereafter. The study at hand represents the first global stability analysis of streamwise corner-flow and confirms key observations made in theoretical and/or experimental work on the subject. Namely, the presence of an inviscid instability mechanism in the near-corner region and a destabilising effect of the characteristic mean-flow deformation found in experiment. / <p>QC 20130604</p>

Fracture conductivity and the effects of treatment variables can be studied in the laboratory. We conducted experiments based on scaling down the field conditions to laboratory scale by matching Reynold’s and Peclet numbers. Experiments conducted were comprised of three stages: dynamic etching, surface characterization of etched cores, and conductivity measurement. The effect of initial condition of fracture surfaces on the etching pattern and conductivity were investigated in this study. Another area of interest is the variation of conductivity along the fracture due to acid spending. We also investigated the contact time, acid system type, and treatment temperature effects on conductivity using San Andres dolomite cores. The results from these studies showed that rough-surface fractures generate higher conductivity by an order of magnitude compared with a smooth-surface fracture at low-closure stress. Also, conductivity generated on rough-surface fractures by smoothing peaks and deepening valleys which widen the gap between the fracture surfaces after closure and acid creates conductivity on smooth-surface fractures by differential etching that creates asperities. The results suggest that an increase in acid spending does not automatically result in lower conductivity; and etched volume alone is not adequate to predicate the conductivity. Conductivity results from a combination of etching pattern, etched volume, and rock compressive strength after etching. In-situ crosslinked acid was found to be more effective in etching rock and controlling acid leakoff compared with linear-gelled acid. Also, crosslinked acid reduces the number of pits and the pit diameters. Based on conductivity tests, linear-gelled acid is more favorable at higher temperatures while in-situ crosslinked acid showed higher conductivity at lower temperatures. For a rough-surface fracture, shorter contact time created high conductivity compared to longer contact while injecting the same volume of acid, suggesting the existence of an optimum contact time.

The subject of the submitted thesis „Low pressure water hammer“ is handling the problems of dynamic conduct of water in low pressures. In this work are developed problems of the effect of changing pressure on the speed of sound in liquid. The problem is solved in the time domain using the Lax - Wendroff method in the theoretical analysis. At the end the mathematical model solved using Lax - Wendroff method is confront with the experiment.

For accurate prediction of tsunami wave propagation, information on the system of PDEs modelling its evolution and full initial and/or boundary data is required. However the latter is not generally fully available, and so the primary objective becomes to find an optimal estimate of these conditions, using available information. Data Assimilation is a methodology used to optimally integrate observed measurements into a mathematical model, to generate a better estimate of some control parameter, such as the initial condition of the wave, or the sea floor bathymetry. In this study, we considered the shallow water equations in both linear and non-linear form as an approximation for ocean wave propagation, and derived a data assimilation scheme based on the calculus of variations, the purpose of which is to optimise some distorted form of the initial condition to give a prediction closer to the exact initial data. We considered two possible forms of distortion, by adding noise to our initial wave, and by rescaling the wave amplitude. Multiple cases were analysed, with observations measured at different points in our spatial domain, as well as variations in the number of observation points. We found that the error between measurements and observation data was sufficiently minimised across all cases. A relationship was found between the number of measurement points and the error, dependent on the choice of where measurements were taken. In the linear case, since the wave form simply translates a fixed form, multiple measurement points did not necessarily provide more information. In the nonlinear case, because the waveform changes shape as it translates, adding more measurement points provides more information about the dynamics and the wave shape. This is reflected in the fact that in the nonlinear case adding more points gave a bigger decrease in error, and much closer convergence of the optimised guess for our initial condition to the exact initial wave profile. / Thesis / Master of Science (MSc) / In ocean wave modelling, information on the system dynamics and full initial and/or boundary data is required. When the latter is not fully available the primary objective is to find an optimal estimate of these conditions, using available information. Data Assimilation is a methodology used to optimally integrate observed measurements into a mathematical model, to generate a better estimate of some control parameter, such as the initial condition of the wave, or the sea floor bathymetry. In this study, we considered the shallow water equations in both linear and non-linear form as an approximation for ocean wave propagation, and derived a data assimilation scheme to optimise some distorted form of the initial condition to generate predictions converging to the exact initial data. The error between measurements and observation data was sufficiently minimised across all cases. A relationship was found between the number of measurement points and the error, dependent on the choice of where measurements were taken.

The effect of chamber length and Reynolds number on the stability and behavior of the flow field generated by a precessing jet nozzle was studied using stereoscopic particle image velocimetry (StereoPIV). An algorithm was developed to determine the mode of the flow based on the distribution of axial velocity. The optimal chamber length for precession to occur was found to be between 2 and 2.75 chamber-diameters. There is no precession at a chamber length of one diameter, and the occurrence of precession was found to be strongly related to Reynolds number. Conditionally averaged velocity distributions for the flow in precessing mode were calculated. The effect of initial condition on downstream behavior of axisymmetric jets was examined. Variations in spread and decay rates were found for jets issuing from different nozzles. Self-similar solutions for axisymmetric jets are therefore not universal, and are instead dependent upon initial conditions at the source.

No description available.

We investigate a system of nonlinear partial differential equations, specifically the so-called Ladyzhenskaya model, in three spatial dimensions. It will be shown that after inclusion of a perturbation of a higher order, the model exhibits a considerably better behavior, in particular it will become quite straightforward to prove differentiability of solutions with respect to the initial condition. Due to this fact we may consequently employ the method of Lyapunov exponents to estimate the fractal dimension of the exponential attractor. First, however, it will be necessary to show existence and uniqueness of solutions, improved regularity and existence of a compact invariant set for the entire system.

Submitted by Irene Nascimento (irene.kessia@ufpe.br) on 2017-03-29T19:13:09Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Tese-Thamires.pdf: 818214 bytes, checksum: 5697cce4e93e09e89c5150c064df333e (MD5) / Made available in DSpace on 2017-03-29T19:13:09Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Tese-Thamires.pdf: 818214 bytes, checksum: 5697cce4e93e09e89c5150c064df333e (MD5) Previous issue date: 2016-02-26 / CNPQ / Este trabalho trata da teoria de existência, unicidade, regularidade, continuação e alternativa de Blow-up de solução brandas para Equação de Volterra Fracionarias com condições iniciais locais cujo termo não linear satisfaz certas propriedades localmente Lipschitz. Analisamos também o caso de condições iniciais não locais e não linearidades verificando condições do tipo Caratheodory. Neste caso estudamos as propriedades topológicas do conjunto soluções de tais equações. / his work deals with existence, uniqueness, regularity, continuation and Blow up Alternative of mild solutions for Fractional Volterra Equations with local initial conditions, whose nonlinear terms satisfy some locally Lipschitz properties. Moreover we analyse thecase of nonlocal initial conditions and nonlinearities of Caratheodory type. In this case, we study topological properties of the solution set of such equations.

In this diploma thesis called Water column separation under the hydraulic turbine runner during unsteady operating regimes are solved the pressure pulsations of the reverse water hamer. In the thesis is deduced a mathematical relationship of elaboration the numerice model which is based on equations of continuity and equations of forces equilibrium. Numerical model is created in MS Excel uses for computation the numerical method Lax-Wendrof that allows consideration of variable sound speed as function of static pressure and allows variable lenght step in computation domain. Reverse water hammer is in the thesis solved with consideration of rotating flow behind shut-off valve, where we expect forming of vortex rope. This situation can be applied on the closing water turbine which has vertex rope under turbine runner. Specifically for this thesis was carried out the experiment of the reverse water hammer. Constants going into numerical solution are optimalized with using experiment and pressure pulsation are compared between numerical solution and experiment.

Engineers frequently use computerized numeric models to calculate and predict water levels and current patterns for rivers, bays, and other bodies of water. This computation often involves an iterative process known as incremental loading that can cause frustration and consume a lot of time. Although the steering module in the Surface-water Modeling System (SMS) automates incremental loading to minimize user interaction, it can still be very time consuming. This thesis examines the steering module and the incremental loading process to improve its efficiency. Specifically, the RMA2 and FESWMS models are utilized. Two methods of improving efficiency are examined. The first includes creating predicted solution files for each step of the incremental loading process. These predictions allow the steering module to take larger steps and decrease the computation time. The second method changes the algorithm used to determine the size of each step. Finally, the interface to the process was examined and simplified to require minimal input and to make the input more intuitive.