Existence and stability of nonmonotone hydraulic shocks for the Saint Venant equations of inclined thin-film flow

Extending work of Yang-Zumbrun for the hydrodynamically stable case of Froude number F < 2, we categorize completely the existence and convective stability of hydraulic shock profiles of the Saint Venant equations of inclined thin-film flow. Moreover, we confirm by numerical experiment that asymptotic dynamics for general Riemann data is given in the hydrodynamic instability regime by either stable hydraulic shock waves, or a pattern consisting of an invading roll wave front separated by a finite terminating Lax shock from a constant state at plus infinity. Notably, profiles, and existence and stability diagrams are all rigorously obtained by mathematical analysis and explicit calculation

Stability of Viscous St. Venant Roll-Waves: From Onset to the Infinite-Froude Number Limit

International audienceWe study the spectral stability of roll-wave solutions of the viscous St. Venant equationsmodeling inclined shallow-water flow, both at onset in the small-Froude number or “weakly unstable”limit F → 2+ and for general values of the Froude number F , including the limit F → +∞. In the former,F → 2+ , limit, the shallow water equations are formally approximated by a Korteweg de Vries/Kuramoto-Sivashinsky (KdV-KS) equation that is a singular perturbation of the standard Korteweg de Vries (KdV)equation modeling horizontal shallow water flow. Our main analytical result is to rigorously validate thisformal limit, showing that stability as F → 2+ is equivalent to stability of the corresponding KdV-KSwaves in the KdV limit. Together with recent results obtained for KdV-KS by Johnson–Noble–Rodrigues–Zumbrun and Barker, this gives not only the first rigorous verification of stability for any single viscous St.Venant roll wave, but a complete classification of stability in the weakly unstable limit. In the remainderof the paper, we investigate numerically and analytically the evolution of the stability diagram as Froudenumber increases to infinity. Notably, we find transition at around F = 2.3 from weakly unstable todifferent, large-F behavior, with stability determined by simple power law relations. The latter stabilitycriteria are potentially useful in hydraulic engineering applications, for which typically 2.5 ≤ F ≤ 6.0

Whitham's Modulation Equations and Stability of Periodic Wave Solutions of the Korteweg-de Vries-Kuramoto-Sivashinsky Equation

International audienceWe study the spectral stability of periodic wave trains of the Korteweg-de Vries-Kuramoto-Sivashinsky equation which are, among many other applications, often used to describe the evolution of a thin liquid film flowing down an inclined ramp. More precisely, we show that the formal slow modulation approximation resulting in the Whitham system accurately describes the spectral stability to side-band perturbations. Here, we use a direct Bloch expansion method and spectral perturbation analysis instead of Evans function computations. We first establish, in our context, the now usual connection between first order expansion of eigenvalues bifurcating from the origin (both eigenvalue 0 and Floquet parameter 0) and the first order Whitham's modulation system: the hyperbolicity of such a system provides a necessary condition of spectral stability. Under a condition of strict hyperbolicity, we show that eigenvalues are indeed analytic in the neighborhood of the origin and that their expansion up to second order is connected to a viscous correction of the Whitham's equations. This, in turn, provides new stability criteria. Finally, we study the Korteweg-de Vries limit: in this case the domain of validity of the previous expansion shrinks to nothing and a new modulation theory is needed. The new modulation system consists in the Korteweg-de Vries modulation equations supplemented with a source term: relaxation limit in such a system provides in turn some stability criteria

Proceedings of the XVIIIth Telemac & Mascaret User Club 2011, 19-21 October 2011, EDF R&D, Chatou

Water Qualit

Occurrence and Energy Dissipation of Breaking Surface Waves in the Nearshore Studied with Coherent Marine Radar

Wave breaking influences air-sea interactions, wave induced forces on coastal structures, sediment transport and associated coastline changes. A good understanding of the process and a proper incorporation of wave breaking into earth system models is crucial for a solid assessment of the impacts of climate change and human influences on coastal dynamics. However, many aspects are still poorly understood which can be attributed to the fact that wave breaking is difficult to observe and study because it occurs randomly and involves multiple spatial and temporal scales. Within this doctoral work, a nearshore field experiment was planned and conducted on the island of Sylt in the North Sea to investigate the dynamics of wave breaking. The study combines in-situ observations, numerical simulations and remote sensing using shore-based coherent marine radar. The field measurements are used to investigate the coherent microwave backscatter from shoaling and breaking waves. Three major developments result from the study. The first one is a forward model to compute the backscatter intensity and Doppler velocity from known wave kinematics. The second development is a new classification algorithm to identify dominant breakers, whitecaps and radar imaging artifacts within the radar raw data. The algorithm is used to infer the fraction of breaking waves over a sub- and an inter-tidal sandbar as well as whitecap statistics and results are compared to different parameterizations available in literature. The third development is a new method to deduce the energy of the surface roller from the Doppler velocity measured by the radar. The roller energy is related to the dissipation of roller energy by the stress acting at the surface under the roller. From the spatial gradient of roller energy, the transformation of the significant wave height is computed along the entire cross-shore transect. Comparisons to in-situ measurements of the significant wave height from two bottom mounted pressure gauges and a wave rider buoy show a total root-mean-square-error of 0.20 m and a bias of −0.02 m. It is the first time that measurements of the spatio-temporal variation of the bulk wave energy dissipation together with the fraction of breaking waves are achieved in storm conditions over such a large distance of more than one kilometer. The largest dissipation rates (> 300 W/m² ) take place on a short distance of less than one wave length (≈ 50 m) at the inter-tidal sandbar. However, during storm conditions 50 % of the incoming wave energy flux is already dissipated at the sub-tidal sandbar. The simultaneous measurements of the occurrence frequency and the energy dissipation facilitate an assessment of the bulk dissipation of individual breaking waves. For the spilling-type breakers in this area, the observed dissipation rate is about 30 % smaller than the dissipation rate according to the generally used bore analogy. This must be considered within nearshore wave models if accurate predictions of the breaking probability are required

Modélisation expérimentale des écoulements transitoires avec poches d'air emprisonnées dans les réseaux de drainage urbain

RÉSUMÉ Les eaux pluviales urbaines sont évacuées par des réseaux de drainage qui sont conçus pour fonctionner en écoulement à surface libre. Or pour plusieurs raisons, comme une augmentation de l’intensité de la pluie ou de sa fréquence, une urbanisation accrue, ou des dysfonctionnements dans le réseau, la capacité d’évacuation de la conduite peut être dépassée. Ce dépassement de capacité entraine une mise en charge partielle ou totale de la conduite. Le passage d’un écoulement à surface libre vers un écoulement en charge ou vice-versa représente un type d’écoulement appelé « écoulement transitoire ». Durant un écoulement transitoire, on observe des variations importantes de pression et de vitesse pouvant créer des dommages tels qu’une rupture de conduites, un effondrement d’infrastructures, une inondation de zones bases, une apparution de geyzers, etc. Ces écoulements transitoires sont très souvent accompagnés d’une entrée/évacuation de quantités importantes d’air dans le réseau. Pour améliorer la conception des nouveaux réseaux de drainage et la réhabilitation des réseaux existants, les modèles de simulation doivent prendre en compte les écoulements transitoires en intégrant des aspects particuliers souvent négligés, notamment la dynamique de l’écoulement et les effets de l’air. C’est dans ce cadre que le Laboratoire d’Hydraulique de l’École Polytechnque a mis en place un programme qui vise la modélisation numérique et physique (expérimentale) des écoulements transitoires avec et sans poches d’air emprisonnées. Le présent mémoire rentre dans le cadre ce programme. Son objectif principal est de faire une analyse dynamique et expérimentale des écoulements transitoires avec poches et bulles d’air,dans le but de disposer d’éléments de comparaison et de pistes de solution pour la réalisation du odèle numérique particulièrement dans sa composante avec poches d’air. La principale hypothése émise durant cette étude est que l’effet de l’air, souvent négligé, a un impact certain sur la dynamique de l’écoulement. Les travaux de ce mémoire se structurent en trois grandes parties : une revue bibliographique, un travail numérique sur le modèle de simulation en cours de réalisation et des travaux expérimentaux.----------ABSTRACT Urban stormwaters are removed through sewer systems that are designed to operate in free surface flow. But for several reasons, such as increased intensity of rainfall or its frequency, increased urbanization, hydraulic failures, the pipe capacity may be exceeded. This overflow causes a partial or total pressurization pipe. The passage of free surface flow to pressurized flow is part of transient flows, during which the pressure and velocity variations are fast and can create damage such as the collapse of infrastructure, the ‘blow-off’ of manhole covers, geysers, and basement flooding, etc. These transient flows are often accompanied by entrance and release a large amount of air in sewers. To improve the design of new drainage systems and rehabilitation of existing sewers, taking into account the transient flows, simulation models should incorporate aspects often neglected, including the flow dynamics and air effects. For the reason the Hydraulics Laboratory of “École Polytechnique de Montreal” has implemented a program to construct a transient flows simulation model with and without air pockets. This master aims to make a dynamic analysis and experimental study of transient flows with air pockets and bubbles,in order to provide data for comparison and possible solutions for the realization of numerical model especially in its component with air pockets. The main hypothesis emitted during this study is that the air effect, often overlooked, strongly impacts the flow dynamics. This work is structured into three main parts: literature review, numerical work on the numerical model in progress and experimental work. i) The literature review has enabled a critical analysis of existing models and develops their strengths and limitations. These models are classified according to the calculation method (Preissmann slot, interface tracking or two-compnent pressure approach) and for their ability to take into account the air effect. This review has shown that there is a diverse range of models, yet none of these takes fully into account the flow dynamics particularly as a result of the air

Oscillations of cylinders in waves and currents

This thesis contains the results of two research investigations conducted by the author, the first an exploratory investigation into wave induced vibrations, conducted at the British Hydrodynamics Research Association (BHRA), and the second a comprehensive investigation into the forces on cylinders oscillated in still water and inline with various currents, conducted at the River and Harbour Laboratory (VHL), Trondheim, Norway. Questions posed by the results of the first investigation were used in the formulation of the second, and results from the second led to a better understanding of the first