| his thesis investigates the consequences of the presence of smooth Lagrangian chaotic flows in two different physical systems described by formally similar equations. In an electrically conducting fluid, chaotic flows are responsible for magnetic field instabilities, whereas in a standard Navier-Stokes fluid, they lead to instabilities of the vorticity field. These instabilities are central to the understanding of, respectively, the origin of large magnetic fields in stars and, to a certain extent, the mechanism of onset of turbulence.;The first part tests previous heuristically derived general theoretical results for the fast kinematic dynamo instability of a smooth, chaotic flow by comparison of the theoretical results with numerical computations on a particular class of model flows. The class of chaotic flows studied allows very efficient high resolution computation. It is shown that an initial spatially uniform magnetic field undergoes two phases of growth, one before and one after the diffusion scale has been reached. Fast dynamo action is obtained for large magnetic Reynolds number (;In the second part, we show that at high Reynolds number, smooth, Lagrangian chaotic flows are typically linearly unstable and that the perturbed vorticity tends to concentrate on a fractal. Numerical integration of the relevant linear partial differential equations with Reynolds number up to... |
