The study of wave production and propagation is a common phenomenon seen within a variety of math and physics problems. This thesis in particular will investigate the production and propagation of sound waves through musical instruments. Although this field of work has been examined since the late 1800s, approaching these types of problems can be very difficult. With the exception of the last fifty years, we have only been able to approach such problems by linearizing the necessary equations of gas dynamics. Without the use of a computer, one can only get so far in studying nonlinear acoustic problems. In addition, the numerical theory for nonlinear problems is incomplete. Proving stability is challenging and there are a variety of open problems within this field. This thesis will be examining the propagation of sound waves specifically through brass instruments. However, we will not be able to fully examine this problem in a master’s thesis because of the complexity. Instead, the objective is to provide a foundation and global picture of this problem by merge the fields of nonlinear acoustics as well as computational and analytical gas dynamics. To study the general behaviour of nonlinear wave propagation (and to verify previous findings), experiments have been carried on a trumpet. The purpose of these experiments is take measurements of the sound pressure waves at various locations along the instrument in order to understand the evolution of the wave propagation. In particular, we want to establish if the nonlinear distortion is strong enough to have musical consequences; and if there are such outcomes, what prerequisites are required for the observable behaviour. Additionally, by using the discontinuous Galerkin numerical method, a model of the system will be presented in this thesis. It will then be compared with the experimental data to verify how well we were able to describe the nonlinear wave motion within a trumpet.

Orientador: Geraldo de Freitas Maciel / Banca: José Luiz Gasche / Banca: José Carlos Cesar Amorim / Resumo: Os escoamentos em superfície livre que ocorrem em canais inclinados, tanto em fluido Newtoniano quanto em fluido não-Newtoniano (hiperconcentrado), podem desenvolver instabilidades, tais como ondas em forma de ressalto hidráulico, com comprimentos bem definidos. Tais perturbações são denominadas Roll Waves. Essas ondas são comuns em canais artificiais, em lavas torrenciais e deslizamento de avalanchas. Neste trabalho, no plano teórico, é determinado um modelo matemático geral, com base nas equações de Navier- Stokes integradas na vertical, em cujo tensor de tensões é introduzido a reologia de Herschel- Bulkley. A velocidade média do escoamento é determinada levando-se em consideração que o escoamento apresenta um perfil de velocidade parabólico na região cisalhada (próximo ao fundo do canal) acoplado a um perfil linear na região não cisalhada (condição de plug), característico dos escoamentos de lamas e detritos. A partir do sistema de equações (conservação da massa e equação da quantidade de movimento) em variáveis adimensionais, uma análise de estabilidade linear é realizada, colocando em evidência as condições de formação dessas instabilidades, tanto em fluido hiperconcentrado como em fluido Newtoniano. Com as condições de formação de instabilidades estabelecidas, uma teoria analítica de Roll Waves permanente é imposta e um modelo matemático para geração de tais instabilidades é determinado. No plano numérico, utilizando a linguagem de programação Python, a validade do modelo é verificada, considerando que essas ondas são ajustadas por choques devido às singularidades existentes no modelo. Com a determinação das condições de choque e da velocidade de propagação da onda em um ponto crítico; pode-se observar a formação de Roll Waves em fluidos não Newtonianos com reologia de Herschel-Bulkley, Bingham, Power Law, como também em fluido Newtoniano. / Abstract: The flows in free surface that occur in sloping canals, such as Newtonian fluid as in non- Newtonian fluid (hyperconcentrated), they can develop instabilities, such as long waves in form of hydraulical jumps, with well defined lengths; these instabilities are called Roll Waves, more common in artificial canals, torrential spillways of dams, lava and avalanche landslide. This work, in the theoretical plan, a general mathematical model is determined, on the basis of the integrated Navier-Stokes equation in the vertical, of tensor tensions the rheology of Herschel-Bulkley is introduced. The average velocity of the flows is determined taking itself in consideration that the flows presents a parabolic profile of speed in the shear region (near of the floor of canal) connected to a linear profile in the region not shear (condition of plug), categorized as flows of mudflows and debris flows. From the system of equations (conservation of the mass and equation of the momentum) in adimensional variables, an analysis of linear stability is carried through, placing the conditions of formation of these instabilities, as much in hyperconcentrated fluid as in Newtonian fluid. With the conditions of formation of instabilities established, a analytical theory of permanent Roll Waves is imployed and a mathematical model for geration of such stabilities it's determined. In the numerical plan, using the computational consol Python, the validity of model is checked, considering of this waves are adjusted by shocks devided by the singularities existents in the model. With the determination of conditions of shock and the velocity of propagation of wave in a critical point; we can observe the formation of Roll Waves such in fluids non-Newtonians (Herschel- Bulkley, Bingham, Power law) as Newtonian fluids. / Mestre

Recent observations have shown that coronal shocks driven by coronal mass ejections can develop and accelerate particles within several solar radii in large solar energetic particle (SEP) events. Motivated by this, we present an SEP acceleration study that including the process in which a fast shock propagates through a streamer-like magnetic field with both closed and open field lines in the low corona region. The acceleration of protons is modeled by numerically solving the Parker transport equation with spatial diffusion both along and across the magnetic field. We show that particles can be sufficiently accelerated to up to several hundred MeV within 2-3 solar radii. When the shock propagates through a streamer-like magnetic field, particles are more efficiently accelerated compared to the case with a simple radial magnetic field, mainly due to perpendicular shock geometry and the natural trapping effect of closed magnetic fields. Our results suggest that the coronal magnetic field configuration is an important factor for producing large SEP events. We further show that the coronal magnetic field configuration strongly influences the distribution of energetic particles, leading to different locations of source regions along the shock front where most high-energy particles are concentrated. This work may have strong implications for SEP observations. The upcoming Parker Solar Probe will provide in situ observations for the distribution of energetic particles in the coronal shock region, and test the results of the study.

Cette thèse traite des effets de la turbulence atmosphérique sur la propagation d'ondes de choc acoustiques. Ces effets sont d'un grand intérêt pour des applications comme le bang sonique, le buzz saw noise ou le tonnerre. Une méthode numérique unidirectionnelle est développée pour modéliser et simuler la propagation tridimensionnelle d'ondes de choc acoustiques en milieu hétérogène en mouvement. Elle repose sur une approche à pas fractionnés qui permet de prendre en compte efficacement les différents mécanismes physiques présents. Pour s'attaquer à des problèmes 3D réalistes (de l'ordre du milliard de degré de liberté), l'implémentation de la méthode est réalisée en utilisant le paradigme de programmation parallèle " single program multiple data ". La validité de cette méthode est évaluée sur différents cas tests. La méthode est appliquée à l'étude des effets de la turbulence atmosphérique sur la propagation du bang sonique dans la couche limite planétaire. Ainsi, le bang sous trace et le bang dans la zone d'ombre sont calculés pour la configuration hypersonique développée dans le projet européen ATLLAS II. Enfin, la focalisation de chocs faibles sur une caustique cuspidée est simulée. Cela est, à notre connaissance, la première étude de la stabilité d'une caustique non linéaire à des perturbations dues à un écoulement. / This thesis deals with the effects of atmospheric turbulence on the propagation of acoustical shock waves. These effects are of major interest for applications such as sonic boom, buzz saw noise or thunder. A numerical one-way method is developed to model and to simulate three-dimensional nonlinear propagation of acoustical shock waves in a moving heterogeneous medium. It relies on a split-step approach that permits to take into account efficiently the different involved physical mechanisms. To tackle realistic 3D problems (of order of one billion of degree of freedom), the implementation of the method is done using the parallel single program multiple data paradigm. Validity of this method is assessed using multiple test cases. The method is applied to investigate the effects of atmospheric turbulence on sonic boom propagation through the Planetary Boundary Layer. Hence, both under-track boom and boom in the shadow zone are studied for a hypersonic configuration developed in the European project ATLLAS II. Finally, the focusing of weak shock waves on a cusped caustic is simulated. It is the first study of the stability of a nonlinear caustic to flow perturbations to our knowledge.

Le choc laser est un procédé de plus en plus répandu qui utilise l’énergie laser pour générer des ondes de choc et inclure des effets mécaniques dans les matériaux ciblés. Lorsque l’énergie laser est absorbée par la cible, un plasma d’interaction est créé à la surface du matériau. Ce plasma, lors de sa détente, génère une onde de choc qui se propage. Les travaux effectués dans le cadre de cette thèse s’inscrivent donc dans une démarche globale de compréhension des phénomènes liés à l’interaction laser-matière. Dans le domaine des ondes de choc générées par laser, on peut distinguer deux procédés : Le traitement de surface par choc laser (LSP - Laser Shock Peening) et le test d’adhérence par choc laser (LASAT - LASer Adhesion Technique). Aujourd’hui la question se pose sur les limitations des procédés de choc par laser et sur les solutions à mettre en place pour pallier à ces limitations. Des idées sur l’amélioration des confinements, comme substitution à l’eau, ou encore l’optimisation des revêtements protecteurs ont été proposées. Par ailleurs, au cours de ces travaux de thèse, l’utilisation de deux impulsions laser a permis, dans le cas du procédé LASAT, l’optimisation de la traction générée aux interfaces des multimatériaux et ainsi de rendre le procédé plus robuste. De plus, dans le cas du procédé LSP, les aspects de rentabilité liés à la cadence de traitement ont été étudiés. Finalement, que ce soit pour les décalages en temps faibles (entre 0 et 1000 ns) ou bien les décalages importants (entre 200µs à 200ms), l’étude des phénomènes liés à l’interaction laser-matière a permis de franchir certaines limitations pour les deux procédés. / The laser shock wave generation is a novel process becoming more and more common. The shock waves are used to generate mechanicals effects in the sample. The laser absorption results in the creation of a plasma at the surface. This plasma during its expansion creates a shock wave propagating through the sample. This work aims to study the various phenomena involved in the laser-matter interaction. In the field of laser generated shock waves, two different processes exist: the Laser Shock Peening (LSP) and the LASer Adhesion Technique (LASAT). The new challenge deals with the limitations of those processes and the solutions to be setting up to improve them. Some ideas concerning the confinement improvement as water substitution or thermal coatings optimization are suggested in this work. Moreover, the use of double delayed laser pulses allows, for LASAT, the location of main tensile stresses near interfaces. However, for LSP, some aspects dealing with the profitability linked to the peening rate are investigated here. Last but not least, whether the very short (0 to 1000 ns) or very long delays (from 200µs to 200ms), the study of the laser-matter interaction phenomena allows to overcome some limitations for both laser shock processes.

Pas de résumé / Propagation of nonlinear acoustic waves in inhomogeneous media is an important problem inmany research domains of modern theoretical and applied acoustics. For example, studies onpropagation of high amplitude N-waves in turbulent atmosphere are relevant to the sonic boomproblem which involves high interest due to development of new civil supersonic aircrafts. Inrelation to sonic boom problem, many studies on spark-generated N-wave propagation through aturbulent layer were carried out in model laboratory-scale experiments which are more controlledand reproducible than field measurements. Propagation of high intensity focused ultrasound intissue (HIFU) is intensively studied for medical applications. HIFU is a basis of new surgicaldevices for noninvasive thermal and mechanical ablation of tumors.In this thesis, the problem of characterization of high amplitude N-waves generated in air byan electric spark was studied using combined acoustical and optical methods. The fine structureof shocks was deduced from the shadowgraphy images with a resolution that cannot be obtainedusing condenser microphones. It was shown that the combination of optical and acoustical methodsallows complete characterization of the N-waves.N-wave propagation through a layer of thermal turbulence was further studied in a laboratoryexperiment. The evolution of statistical distributions and average values of the most importantN-wave parameters was investigated at different propagation distances. Experimental results werecompared to data obtained in another experiment known in literature, where N-wave was propagatedthrough kinematic turbulence. It was shown that in the case of almost the same widths ofthe turbulent layers, values of the characteristic scales and rms of refractive index fluctuations, thekinematic turbulence leads to stronger distortions of the peak pressure and the shock rise time ofthe N-wave and to 2-3 greater probabilities to observe intense focusing in caustics.Effects of nonlinear propagation and random focusing on the statistics of N-wave amplitudewere studied theoretically using the KZK equation and the phase screen model. The phase screenwas characterized by the correlation length and the refraction length – the distance where firstcaustics occur. Probability distributions, mean values and standard deviations of the N-wave peakpressure were obtained from the numerical solutions and were presented as functions of the propagationdistance and the nonlinear length. Statistical results from the KZK model were comparedwith analytical predictions of the nonlinear geometrical acoustics approach (NGA). It was shown,that NGA approach is valid only up to the distance of one third of refraction length of the screen.Strong nonlinear effects were shown to suppress amplitude fluctuations. The effect of the scale ofinhomogeneities on amplitude statistics was also investigated.The problem of focusing of ultrasound beam through inhomogeneous medium is importantfor medical diagnostics and nondestructive testing problems. The inhomogeneities of biologicaltissue or of industrial materials can destroy beam focusing. In the thesis, distortions of a weaklynonlinear diagnostic beam focused through a phase layer of special configuration were consideredexperimentally and theoretically. Feasibility of selective destruction of focusing of differentharmonics in the beam was predicted in the modeling and confirmed in experiment.The most modern HIFU devices rely on using two-dimensional multi-element phased arrayswith elements randomly distributed over a segment of a spherical surface. Numerical experimentis an important tool to characterize pressure fields created by HIFU radiators. Intensity levels atthe focus of HIFU radiators can reach several tens of thousands of W/cm2, causing nonlinearpropagation effects and formation of shocks [...]

Shock waves are generally characterized by a sharp change of the pressure, which causes subsequent changes in properties of the surrounding in which it spreads. In medical applications, it is an acoustic shock wave which is used for the treatment of concrements for more than 25 years. This success naturally led to considerations about the possibility of using shock waves in other areas of medicine. One of the main directions of the research is the possibility of the damage to tumor tissue. In contrast to concrements the tumor tissue is not different from surrounding tissues by its acoustic attributes, so the normal lithotryptor is not appropriate for this application. Therefore, there has been developed a new source of shock waves, which is based on the principle of multichannel discharge on the composite anode. The experiments demonstrated the effect of the new source on the acoustically homogeneous tissue of the thigh muscle at a depth of rabbit in vivo. Then there was observed the damage to tumor tissue in vivo in rats. Finally, there was observed the damage to tumor tissue in vivo in rats in the combination with cisplatin and Photosan. It was found that the new source of shock waves can cause the damage to the acoustically homogeneous tissue in vivo in depth. It also can damage the tumor...

Un nouveau code de simulation numérique pour la propagation des ondes de choc acoustiques dans des géométries complexes a été développé. Le point de départ a été la méthode de Galerkin discontinu qui utilise des maillages non structurés (ici des éléments triangulaires), particulièrement adaptés aux géométries complexes. Cependant, cette discrétisation conduit à l'apparition d'oscillation de Gibbs. Pour pallier ce problème, nous avons choisi d'introduire de la viscosité artificielle au voisinage des chocs. Cela a nécessité le développement de trois outils originaux : (i) un nouveau détecteur de choc sensible aux ondes de chocs acoustiques sur des maillages non structurés, (ii) un nouveau terme de viscosité artificielle dans les équations de l'acoustique non linéaire défini élément par élément et (iii) un nouveau terme permettant de régler le niveau de viscosité locale à partir du raidissement des fronts d'onde. Le code de calcul a été utilisé pour étudier deux configurations différentes. La première concerne la réflexion d'ondes de choc acoustiques sur des surfaces rigides. Différents régimes de réflexion ont alors été observés allant, de la réflexion classique de Snell Descartes jusqu'à celui dit de réflexion faible de Von Neumann. La deuxième configuration était consacrée à la focalisation d'ondes de choc acoustiques produites par un transducteur à haute intensité (comme ceux utilisés en HIFU). Un soin particulier a été pris pour étudier le calcul de l'intensité et pour étudier l'interaction entre les ondes de choc et des obstacles placés dans la région du foyer. / A new numerical solver for the propagation of acoustical shock waves in complex geometry has been developed. This is done starting from the discontinuous Galerkin method. This method is based on unstructured mesh (triangular elements here), and so, naturally it is well-adapted for complex geometries. Nevertheless, the discretization induces Gibbs oscillations. To manage this problem, we choose to introduce some artificial viscosity only in the vicinity of the shocks. This necessitates the development of three original tools. First of all, a new shock sensor for unstructured mesh sensitive to acoustical shock waves has been designed. It senses where the local artificial viscosity has to be introduced thanks to a reformulation of a new element centred smooth artificial viscosity term in the equations. Finally, the amount of viscosity is computed by the introduction of an original notion of gradient factor linked to the steepening of the waveform. The numerical solver has been used to investigate two different physical situations. The first one is the nonlinear reflection of acoustical shock waves on rigid surfaces. Different regimes of reflection have been observed ranging from the linear Snell Descartes reflection to the weak von Neumann case. The second configuration deals with the focusing of shock waves produced by high intensity transducers (like in HIFU). Special attention has been given to the careful computation of intensity and to the interaction between the shock waves and obstacles in the region of the focus.

This thesis considers linear perturbations to the steady flow of a compressible inviscid perfect gas along a cylindrical or annular duct. Particular consideration is given to the model of the duct boundary, and to the effect of curvature of the duct centreline. For a duct with a straight centreline and a locally-reacting boundary, the acoustic duct modes can be segregated into ordinary duct modes and surface modes. Previously-known asymptotics for the surface modes are generalized, and the generalization is shown to provide a distinctly better approximation in aeroacoustically relevant situations. The stability of the surface modes is considered, and previous stability analyses are shown to be incorrect, as their boundary model is illposed. By considering a metal thin-shell boundary, this illposedness is explained, and stability analysed using the Briggs-Bers criterion. The stability of a cylindrical thin shell containing compressible fluid is shown to differ significantly from the stability for an incompressible fluid, even for parameters for which the fluid would otherwise be expected to behave incompressibly. The scattering of sound by a sudden hard-wall to thin-shell boundary change is considered, using the Wiener-Hopf technique. The causal acoustic field is derived analytically, without the need to apply a Kutta-like condition or to include an instability wave, as had previously been necessary. Attention is then turned to a cylindrical duct with a curved centreline and either hard or locally-reacting walls. The centreline curvature (which is not assumed small) and wall radii vary slowly along the duct, enabling an asymptotic multiple scales analysis. The duct modes are found numerically at each axial location, and interesting characteristics are explained using ray theory. This analysis is applied to a hard-walled RAE 2129 duct, and frequency-domain solutions are convolved to give a time-domain example of a pulse propagating along this duct. Finally, some numerical work on the nonlinear propagation of a large-amplitude pulse along a curved duct is presented. This is aimed at modelling a surge event in an aeroengine with a convoluted intake.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第22254号 / 理博第4568号 / 新制||理||1656(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 一本 潔, 准教授 浅井 歩, 教授 柴田 一成 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM