A predictive methodology for received signal variation as a function of ocean perturbations is developed using a ray-based analysis of the effects of internal waves and ocean turbulence on long and short range underwater acoustic propagation. In the present formulation the eikonal equations are considered in the form of a second-order, nonlinear ordinary differential equation with harmonic excitation due to an internal wave. The harmonic excitation is taken imperfect, i.e., with a random phase modulation due to Gaussian white noise, accounting for both chaotic and stochastic behavior. Simulated turbulence is represented using the potential theory line vortex approach. Simulations are conducted for long range propagation, 1000km, containing internal wave fields with added deterministic effects and are compared to those fields with non-deterministic properties. These results show that long range acoustic propagation has a very strong dependence on the intensity of deterministic fluctuations. Numerical analysis for short range propagation, 10km, was constructed for sound passage through the following perturbation scenarios: simulated turbulence, an internal wave field, and a field of internal waves and simulated turbulence combined. Investigation over varied initial conditions and perturbation strengths suggests internal wave environments supply the majority of spatial variation and turbulent eddy fields are primarily responsible for delay fluctuation. Spectra of the variations in mean travel velocity reveal internal wave dominance to be dependent on the intensity of the wave.

Cette thèse décrit comment les ondes électromagnétiques se propagent dans les plasmas magnétisés, lorsque les fréquences sollicitées sont proches de la fréquence électron cyclotron. Elle porte sur l’analyse mathématique des variétés caractéristiques qui sont associées à des systèmes de type Vlasov-Maxwell relativiste avec paramètres rapides.La première partie s’intéresse aux plasmas froids des magnétosphères planétaires. On explique comment obtenir les relations de dispersion dans le cas d’un dipôle magnétique. Cela conduit à l’étude détaillée de certaines variétés algébriques de l’espace cotangent : les cônes et les sphères dits ordinaires et extraordinaires. La description géométrique de ces cônes et de ces sphères donne accès à une classification complète des ondes électromagnétiques susceptibles de se propager. Diverses applications sont proposées, concernant l’équation eikonale et l’absence de propagation en mode parallèle, ou encore concernant la structure des ondes dites en mode siffleur.La seconde partie porte sur la modélisation des plasmas chauds, typiquement ceux qui sont mis en jeu dans les tokamaks. On prouve dans un contexte réaliste que la propagation des ondes électromagnétiques s’effectue au travers d’un tenseur dielectrique. Ce tenseur est obtenu via une analyse fine des résonances cinétiques qui sont issues des interactions entre les particules (Vlasov) et les ondes (Maxwell). Il s’exprime comme une somme infinie d’intégrales singulières, faisant intervenir l’opérateur de Hilbert. Le sens mathématique de la formule donnant accès à ce tenseur est rigoureusement justifié. / This thesis describes how electromagnetic waves propagate in magnetized plasmas, when the frequencies are in a range around the electron cyclotron frequency. It focuses on the mathematical analysis of the characteristic varieties which are associated with relativistic Vlasov-Maxwell systems involving fast parameters. The first part is concerned with cold plasmas issued from planetary magnetospheres. We explain how to obtain the dispersion relations in the case where the magnetic field is given by a dipole model. This leads to the detailed study of some algebraic varieties from the cotangent space: the so-called ordinary and extraordinary cones and spheres. The geometrical description of these cones and spheres gives access to a complete classification of the electromagnetic waves which can propagate. Various applications are proposed, concerning the eikonal equation and the absence of purely parallel propagation, or concerning the structure of whistler waves. The second part focuses on the modelling of hot plasmas, typically like those involved in tokamaks. We prove in a realistic context that the propagation of electromagnetic waves is governed by some dielectric tensor. This tensor is obtain via some careful analysis of the kinetic resonances, which are issued from the interactions between the particles (Vlasov) and the waves (Maxwell). It can be expressed as an infinite sum of singular integrals, involving the Hilbert transform. The mathematical meaning of the formula defining this tensor is rigorously justified.