Near-resonant triad interactions and wave generation theory are investigated for continuously stratified fluids. Interaction equations are derived for spatially-varying wave trains under the inviscid Boussinesq approximation. Rotational effects are included, and properties of the underlying eigenvalue problem are explored. To facilitate a numerical study of the near-resonant interactions, numerical methods are developed and an analysis of wave generation on a periodic domain is performed. Numerical experiments using laboratory and ocean-scale parameters are conducted, and the simulations confirm the validity of the wave forcing theory. Interaction experiments demonstrate a strong tendency for waves to exhibit nonlinear behaviour. While resonant interactions are observed in the laboratory scale simulations, nonlinear steepening effects and the formation of solitary-like waves dominate the ocean-scale experiments. The results suggest that the weakly-nonlinear interaction theory is only appropriate in a limited parameter regime. The problem of analyzing forced wave equations on an infinite domain is also considered. Motivated by the results obtained on a periodic domain, asymptotic analysis is applied to three important wave equations. The method of steepest descents is used to determine the large-time behaviour for the linearized Korteweg-de Vries, Benjamin-Bona-Mahony, and internal gravity wave equations. The asymptotic results are compared with numerical experiments and found to agree to high precision.

Near-resonant triad interactions and wave generation theory are investigated for continuously stratified fluids. Interaction equations are derived for spatially-varying wave trains under the inviscid Boussinesq approximation. Rotational effects are included, and properties of the underlying eigenvalue problem are explored. To facilitate a numerical study of the near-resonant interactions, numerical methods are developed and an analysis of wave generation on a periodic domain is performed. Numerical experiments using laboratory and ocean-scale parameters are conducted, and the simulations confirm the validity of the wave forcing theory. Interaction experiments demonstrate a strong tendency for waves to exhibit nonlinear behaviour. While resonant interactions are observed in the laboratory scale simulations, nonlinear steepening effects and the formation of solitary-like waves dominate the ocean-scale experiments. The results suggest that the weakly-nonlinear interaction theory is only appropriate in a limited parameter regime. The problem of analyzing forced wave equations on an infinite domain is also considered. Motivated by the results obtained on a periodic domain, asymptotic analysis is applied to three important wave equations. The method of steepest descents is used to determine the large-time behaviour for the linearized Korteweg-de Vries, Benjamin-Bona-Mahony, and internal gravity wave equations. The asymptotic results are compared with numerical experiments and found to agree to high precision.

Dans cette thèse, nous avons considéré les spectres de la molécule CH2=CD2. Dans la partie expérimentale, nous avons enregistré des spectres infrarouges à haute résolution (~ 0,0025 cm-1) et fait une attribution complète des transitions enregistrées. Nous avons pu assigner pour la première fois un grand nombre de transitions des combinaisons peu intenses υ4+υ10, υ4+υ7 et de l'harmonique 2υ10; de bandes interdites par symétrie υ4, υ7+υ10, υ8+υ10; et des bandes «chaudes» υ7+υ10–υ10 et υ8+υ10–υ10. Pour la première fois, plus de 7000 transitions inconnues des bandes fondamentales υ2, υ3, υ6, υ7, υ8, υ10, υ12 et de l'harmonique 2υ7 ont été assignées. Sur la base de la théorie des opérateurs de perturbation et des propriétés de symétrie de la molécule étudiée, nous avons construit un hamiltonien effectif puis ajusté les énergies vibrationnelles expérimentales de quatorze états vibrationnels. De cette étude, il a résulté un écart-type pour l'ajustement d'environ (1,7–2,5)×10−4 cm−1 pour diverses régions spectrales. Nous avons également mesuré les valeurs expérimentales des intensités et des demi-largeurs et avons calculé les paramètres du moment dipolaire effectif et des coefficients d'auto-élargissement de la molécule CH2=CD2. / In this thesis we have considered spectra of the CH2=CD2 molecule. In the experimental part we recorded high-resolution (~ 0.0025 cm-1) infrared spectra and made full assignment of the recorded transitions. We were able to assign for the first time a lot of transitions to the weak combinations υ4+υ10, υ4+υ7 and 2υ10 overtone; forbidden due to the symmetry υ4, υ7+υ10, υ8+υ10; «hot» υ7+υ10–υ10 and υ8+υ10–υ10 bands. More than 7000 previously unknown transitions were assigned to the fundamental bands υ2, υ3, υ6, υ7, υ8, υ10, υ12 and 2υ7 overtone. On the base of operator perturbation theory and the symmetry properties of the studied molecule, we constructed an effective Hamiltonian and then fitted experimental ro-vibrational energies of fourteen vibrational states. As a result, rms-deviation of the fit was about (1.7–2.5)×10−4 cm−1 for various spectral regions. We measured also experimental values of intensities and halfwidths and calculated parameters of effective dipole moment and self-broadening coefficients of the СH2=СD2 molecule.