Modal decomposition of linearized open channel flow

Open channel flow is traditionally modeled as an hyperbolic system of conservation laws, which is an infinite dimensional system with complex dynamics. We consider in this paper an open channel represented by the Saint-Venant equations linearized around a non uniform steady flow regime. We use a frequency domain approach to fully characterize the open channel flow dynamics. The use of the Laplace transform enables us to derive the distributed transfer matrix, linking the boundary inputs to the state of the system. The poles of the system are then computed analytically, and each transfer function is decomposed in a series of eigenfunctions, where the influence of space and time variables can be decoupled. As a result, we can express the time-domain response of the whole canal pool to boundary inputs in terms of discharges. This study is first done in the uniform case, and finally extended to the non uniform case. The solution is studied and illustrated on two different canal pools

Mathematical study of the betaplane model: Equatorial waves and convergence results

We are interested in a model of rotating fluids, describing the motion of the ocean in the equatorial zone. This model is known as the Saint-Venant, or shallow-water type system, to which a rotation term is added whose amplitude is linear with respect to the latitude; in particular it vanishes at the equator. After a physical introduction to the model, we describe the various waves involved and study in detail the resonances associated with those waves. We then exhibit the formal limit system (as the rotation becomes large), obtained as usual by filtering out the waves, and prove its wellposedness. Finally we prove three types of convergence results: a weak convergence result towards a linear, geostrophic equation, a strong convergence result of the filtered solutions towards the unique strong solution to the limit system, and finally a "hybrid" strong convergence result of the filtered solutions towards a weak solution to the limit system. In particular we obtain that there are no confined equatorial waves in the mean motion as the rotation becomes large.Comment: Revised version after referee's comments. Accepted for publication in M\'{e}moires de la Soci\'{e}t\'{e} Math\'{e}matique de Franc

Temporal simulations and stability analyses of elastic splitter plates interacting with cylinder wake flow

Instabilities developing in a configuration constituted by an elastic plate clamped behind a rigid cylinder are analysed in this paper. The interaction between the wake flow generated by the cylinder with the elastic plate leads to self-developing vortex-induced vibrations. Depending of the stiffness of the elastic plate, the plate may oscillate about a non-deviated or a deviated mean transverse position. After having presented non-linear results computed with time-marching simulations, the instabilities are analysed in terms of a fully coupled fluid-structure eigenvalue analysis. We show that the linear stability analysis is able to predict the unstable regions, and provide a good prediction of the unstable vibration frequencies. The mean deviation is characterized by a steady divergence mode in the eigenvalue spectrum, while unstable, unsteady vortex-induced vibration modes show lock-in phenomena

Systems control theory applied to natural and synthetic musical sounds

Systems control theory is a far developped field which helps to study stability, estimation and control of dynamical systems. The physical behaviour of musical instruments, once described by dynamical systems, can then be controlled and numerically simulated for many purposes. The aim of this paper is twofold: first, to provide the theoretical background on linear system theory, both in continuous and discrete time, mainly in the case of a finite number of degrees of freedom ; second, to give illustrative examples on wind instruments, such as the vocal tract represented as a waveguide, and a sliding flute

Improvement of Water Quality in a Highly Polluted River in Jordan

Zarqa River is considered one of the most important sources of surface water in Jordan. The construction of Al-Samra wastewater treatment plant has caused a considerable deterioration in water quality of that river and pollution of the groundwater of that basin. This paper aims to study the change in water quality in the river by applying hydraulic and quality models. Samples of wastewater from the inlet and outlet of the plant were collected and analyzed according to the standard methods. The obtained results concerning BOD, NH4 and DO were used as input to predict water quality in the river. For this purpose, a one dimensional quality model has been developed to simulate pollutants transport in the river. The model was constructed to represent the change in concentrations of such parameters in the river from the treatment plant to the King Talal dam. 296 quality samples and 90 hydraulic samples were taken in order to calibrate the model. Results indicate that the concentrations of BOD, COD and NH4 effluent from the plant exceeded the allowable limits according to Jordanian standards. From the results of simulation, it is found that the model is applied successfully to predict water quality in Zarqa River. Due to self purification, high reduction of pollutant concentrations occur along the river .The concentration of BOD is still higher than the allowable limit until 33 km downstream of the plant, while NH4 concentration is higher than the standards in all reaches

Instrumentation, model identification and control of an experimental irrigation canal

This thesis aims to develop control algorithms for irrigation canals in an experimental framework.These water transport systems are difficult to manage and present low efficiencies in practice. As a result, an important percentage of water is lost, maintenance costs increase and water users follow a rigid irrigation schedule.All these problems can be reduced by automating the operation of irrigation canals.In order to fulfil the objectives, a laboratory canal, called Canal PAC-UPC, was equipped and instrumented in parallel with the development of this thesis. In general, the methods and solutions proposed herein were extensively tested in this canal.In a broader context, three main contributions in different irrigation canal control areas are presented.Focusing on gate-discharge measurements, many submerged-discharge calculation methods are tested and compared using Canal PAC-UPC measurement data. It has been found that most of them present errors around ±10%, but there are notable exceptions. Specifically, using classical formulas with a constant 0.611 contraction value give very good results (errorWith respect to irrigation canal modeling, a detailed procedure to obtain data-driven linear irrigation canal models is successfully developed. These models do not use physical parameters of the system, but are constructed from measurement data. In this case, these models are thought to be used in irrigation canal control issues like controller tuning, internal controller model in predictive controllers or simply as fast and simple simulation platforms. Much effort is employed in obtaining an adequate model structure from the linearized Saint-Venant equations, yielding to a mathematical procedure that verifies the existence of an integrator pole in any type of canal working under any hydraulic condition. Time-domain and frequency-domain results demonstrate the accuracy of the resulting models approximating a canal working around a particular operation condition both in simulation and experiment.Regarding to irrigation canal control, two research lines are exploited. First, a new water level control scheme is proposed as an alternative between decentralized and centralized control. It is called Semi-decentralized scheme and aims to resemble the centralized control performance while maintaining an almost decentralized structure. Second, different water level control schemes based on PI control and Predictive control are studied and compared. The simulation and laboratory results show that the response and performance of this new strategy against offtake discharge changes, are almost identical to the ones of the centralized control, outperforming the other tested schemes based on PI control and on Predictive control. In addition, it is verified that schemes based on Predictive control with good controller models can counteract offtake discharge variations with less level deviations and in almost half the time than PI-based schemes.In addition to these three main contributions, many other smaller developments, minor results and practical recommendations for irrigation canal automation are presented throughout this thesis