Une couche de mélange est généralement considérée comme un prototyped'écoulements libres cisaillés trouve sa présence au sein des nombreuses phénomènesnaturelles et applications industrielles. Le fort développement de l'aéroacoustique, notammentgrâce aux progrès des simulations numériques, a permis d'identifier les structures cohérentesqui se développent dans l'écoulement comme les principales sources de bruit. En outre,l'analyse de stabilité permet de caractériser l'émergence des ondes d'instabilités sous forme deces structures. Dans ce cadre, nous proposons de réaliser à travers ce mémoire une analysede stabilité globale, afin de comprendre l'émergence de fréquences fondamentales, ainsi qu'unedécomposition modale linéaire et non-linéaire, afin de caractériser les structures cohérentesessentiellement responsables du rayonnement acoustique. En particulier, nous proposons dedévelopper les méthodes de stabilité globale en régime compressible ainsi qu'une technique decalcul de structures cohérentes appliquée en régime non-linéaire basée sur la méthode« DMD ». De tels outils d'analyse sont validés et illustrés sur une configuration académiqued'une couche de mélange à co-courant, de type d'amplificateur de bruit, d'un simple cas où uneseule source est impliquée dans le rayonnement acoustique à un cas plus complexe où deuxsources sont présentes. Aussi bien la DMD temporelle que la DMD spatiale sont montréscapables de décrire le comportement des structures cohérentes en champ proche et lescaractéristiques des ondes acoustiques en champ lointain. Enfin, les méthodes dedécomposition modale s'avèrent une base de réduction de modèle pertinente, dans l'objectifd'un contrôle efficace. / A mixing layer is generally considered as a prototype of free shear flows whichoccur in a very broad spectrum of applications from natural phenomena to the engineeringscience. The increasing development of the aeroacoustics, more particularly thanks to theprogress in numerical simulations, has allowed to identify the coherent structures which evolvein the flow as the main sound sources. Furthermore, the emergence of the instability wavestaking the form of the coherent structures can be characterized by the stability analysis. In thiscontext, we propose through this work to perform a global stability analysis, in order tounderstand the emergence of fundamental frequencies, as well as a modal decompositionwithin both a linear and nonlinear framework, to characterize the coherent structures primarilyresponsible for the sound generation. In particular, we propose to develop the methods of theglobal stability with respect to the compressible flows as well as a technique of calculation ofcoherent structures applied to the nonlinear regimes based on the DMD method. Such analysistools are validated and illustrated on an academic configuration of a co-flowing mixing layer, atypical noise amplifier, from a simple case where a single source is implicated in the acousticradiation to a more complex case where two sources are present. Both the temporal and spatialDMD are shown capable of describing the characteristics of the coherent structures in the nearfield and the behaviour of the acoustic waves in the far field. Finally, the methods of the modaldecomposition have proven themselves as a relevant model reduction aiming at designing anefficient control strategy.

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.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第23017号 / 理博第4694号 / 新制||理||1673(附属図書館) / 京都大学大学院理学研究科地球惑星科学専攻 / (主査)准教授 成瀬 元, 准教授 堤 昭人, 教授 生形 貴男 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20917号 / 理博第4369号 / 新制||理||1627(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 嶺重 慎, 准教授 前田 啓一, 教授 太田 耕司 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

No description available.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第24390号 / 理博第4889号 / 新制||理||1699(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 大木谷 耕司, 教授 並河 良典, 准教授 竹広 真一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

No description available.

We exhibit multiple periodic, collision-based orbits of the Newtonian n-body problem. Many of these orbits feature regularizable collisions between the masses. We demonstrate existence of the periodic orbits after performing the appropriate regularization. Stability, including linear stability, for the orbits is then computed using a technique due to Roberts. We point out other interesting features of the orbits as appropriate. When applicable, the results are extended to a broader family of orbits with similar behavior.

In this dissertation, regularization of simultaneous binary collision, existence of a Schubart-like periodic orbit, existence of a planar symmetric periodic orbit with multiple simultaneous binary collisions, and their linear stabilities are studied. The detailed background of those problems is introduced in chapter 1. The singularities of simultaneous binary collision in the collinear four-body problem is regularized in chapter 2. We use canonical transformations to collectively analytically continue the singularities of the simultaneous binary collision solutions in both the decoupled case and the coupled case. All the solutions are found and more importantly, we find a crucial first integral which describes the relationship between the decoupled solutions and the coupled solutions. In chapter 3, we show the existence of a Schubart-like orbit, a periodic orbit with singularities in the symmetric collinear four-body problem. In each period of the orbit, there is a binary collision (BC) between the inner two bodies and a simultaneous binary collision (SBC) of the two clusters on both sides of the origin. The system is regularized and the existence is proven by using a "turning point" technique and a continuity argument on differential equations of the regularized Hamiltonian. Analytical methods are used in chapter 4 to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method can be extended to any even number of bodies. Multiple simultaneous binary collisions are a key feature of the orbits generated. In chapter 5, we apply the analytic-numerical method of Roberts to determine the linear stability of time-reversible periodic simultaneous binary collision orbits in the symmetric collinear four body problem with masses 1, m, m , 1, and also in a symmetric planar four-body problem with equal masses. For the collinear problem, this verifies the earlier numerical results of Sweatman for linear stability.

<p>Different techniques have been employed through the years to predict hydrodynamic instabilities on high speed liquid jets. In this work, a local linear stability analysis (LSA) has been chosen to estimate streamwise wavelengths on the jet surface near the jet exit.  Data for 0.24 to 0.5 diameters downstream in a high speed water jet issuing into air, given by Reynolds number based momentum thickness between 240 and 600, for validation of the method.  </p> <p>The hypothesis is: near the exit of the jet nozzle, for high speed liquid jets, the local velocity profile evolves based on the momentum thickness and, because of large inertia effects, the flow may be considered as inviscid for instability purposes. Therefore, the approach in this work is based on the Rayleigh equation and with the momentum thickness scaling, both non-dimensional and dimensional values of the most unstable wavelengths are obtained.</p> <p>The key aspect of the  approach is the relevance of the momentum thickness as the scaling factor for calculation purposes on dimensional values of wavelengths.</p> <p>Also, a hyperbolic tangent velocity profile is assumed for the Linear Stability Analysis based on the Rayleigh equation. Numerical restrictions and comparisons, using the Riccati transformation, are specified and described in detail to generalize this approach.</p> <p>Results show that analytical estimates of the most unstable streamwise wavelengths are close to the experimental measurements published by Portillo et al. in 2011.  The agreement using this new approach is often within the experimental uncertainty.</p> <p><br></p>