A 2-D fully nonlinear numerical wave tank (NWT) is developed to investigate the Bragg resonance scattered by submerged multi-array breakwaters for random waves. This model is based on a boundary integral equation method with linear element scheme. The fully nonlinear free surface boundary condition is treated using the Mixed Eulerian-Lagrangian method and the 4th-order Runge-Kutta method. The incident random waves are generated by JONSWAP spectrum at one end of the wave tank. Two damping zones are deployed at both ends of the NWT to absorb the energy of the reflected and transmitted waves. In the regular wave cases, the results of Bragg reflection calculated are in good agreement with that of other experiments and numerical models. In addition, the simulated spectrum of random waves is also verified by the original input spectrum. The results of the random waves have the same trend as those of the Regular waves. The reflection coefficient for random waves at the first peak of resonance is about 70 percent of that of the regular wave, but the frequency of band width of Bragg effect has become wider and this advantage may compensate the peak reduction. Finally, we may conclude that the present model is adequate to use as a tool for coastal protection. Systematic studies for random waves propagating over series submerged breakwaters are conducted. The Bragg reflection will be enhanced with the increase of relative height, the length of bars, the number of breakwaters, and the toe angle of submerged breakwaters. In this study, it also reveals that the frequency of peak reflection for higher breakwaters has down shift phenomenon.

Dans cette thèse, nous étudions le volume et la caractéristique d'Euler de sous-variétés aléatoires de codimension r ∈ {1, . . . , n} dans une variété ambiante M de dimension n. Dans un premier modèle, dit des ondes riemanniennes aléatoires, M est une variété riemannienne fermée. Nous considérons alors le lieu Zλ des zéros communs de r combinaisons linéaires aléatoires indépendantes de fonctions propres du laplacien associées à des valeurs propres inférieures à λ 0. Nous obtenons alors les asymptotiques du volume moyen et de la caractéristique d'Euler moyenne de Zλ lorsque λ tend vers l'infini. Dans un second modèle, M est le lieu réel d'une variété projective définie sur les réels. On s'intéresse dans ce cadre au lieu d'annulation réel Zd d'une section holomorphe réelle globale aléatoire de E⊗Ld, où E est un fibré hermitien de rang r, L est un fibré en droites hermitien ample et tous deux sont définis sur les réels. Nous estimons alors les moyennes du volume et de la caractéristique d'Euler de Zd quand d tend vers l'infini. Dans ce modèle algébrique réel, nous calculons aussi l'asymptotique de la variance du volume de Zd pour 1 r < n. Nous en déduisons, dans ce cas, des résultats asymptotiques d'équidistribution de Zd dans M / We study the volume and Euler characteristic of codimension r ∈ {1, . . . , n} random submanifolds in a dimension n manifold M. First, we consider Riemannian random waves. That is M is a closed Riemannian manifold and we study the common zero set Zλ of r independent random linear combinations of eigenfunctions of the Laplacian associated to eigenvalues smaller than λ 0. We compute estimates for the mean volume and Euler characteristic of Zλ as λ goes to infinity. We also consider a model of random real algebraic manifolds. In this setting, M is the real locus of a projective manifold defined over the reals. Then, we consider the real vanishing locus Zd of a random real global holomorphic section of E ⊗ Ld, where E is a rank r Hermitian vector bundle, L is an ample Hermitian line bundle and both these bundles are defined over the reals. We compute the asymptotics of the mean volume and Euler characteristic of Zd as d goes to infinity. In this real algebraic setting, we also compute the asymptotic of the variance of the volume of Zd, when 1 r < n. In this case, we prove asympotic equidistribution results for Zd in M