| The present thesis is devoted to studying spatio-temporal dynamics of non-linear traveling waves. We develop theoretical tools using Bi-Orthogonal Decompositions to understand nonlinear interactions between different components of the wave field under consideration. We study the possible evolutions of uniformly traveling wave as a control parameter varies. Two scenarios have been identified: one involving superpositions of uniformly traveling waves and bifurcations, and one consisting of spatio-temporal modulations of the uniformly traveling waves. We have applied such techniques to convection in binary fluid mixtures in an annular cell, a system which exhibits chaotic wave phenomena. More precisely, we have analyzed sets of experimental data and performed a parameter study of this data base. This experiment has the advantage to be performed with extreme precision and stability. We have shown how our (generic) tools provide quantitative characterization of the complexity arising in this system and how the previous scenarios of uniformly traveling wave destabilization take place. We have studied in detail the Counterpropagating Wave Packets regime and modeled the wave patterns through spatio-temporal modulations model, the dynamics of which agreed well. |
