The magnetohydrodynamics, or dynamo effect, involves the generation of electrical energy from mechanical energy. More specifically, it consists in studying the evolution of a magnetic field generated by a fluid conductor. This phenomenon is found in planets, stars, or even galaxies, where the magnetic field comes from the inner movement. In this thesis, we focus on magnetohydrodynamic instabilities: starting from a conductive fluid with no magnetic field, is a slight disturbance of the flow and magnetic fields (for example, a residue of the magnetic field coming from another system) sufficient to give an amplification of the magnetic field, thus creating a dynamo? The second question consists in the time required to achieve such an amplification of the magnetic field. This thesis is the study of these two questions, and gives two theoretical results and two numerical results.
