In this thesis we developed a Fourier pseudo-spectral code coupled with the volume penalization for the simulation of turbulent MHD flows with non-periodic boundary conditions. This method was validated with classical and academic test-cases. Then we studied the influence of the confinement with walls in a 2D configuration for decaying MHD and we found four decaying regimes which depend on the initial conditions. We also discussed the phenomenon of spontaneous rotation, or spin-up, in 2D non-axisymmetric geometries, originally discovered in hydrodynamic flows. We showed the influence of the Reynolds number and the magnetic pressure on this phenomenon. Finally, simulations of MHD flows in wall bounded three-dimensional domains were addressed. The first results concerning the simulation of decaying MHD turbulence in a cylinder imposing Dirichlet boundary conditions for both the velocity and the magnetic field showed the validity of the code and suggest good prospects for developing more physically justified boundary conditions for the magnetic field.

Magnetohydrodynamics describes dynamics in electrically conductive fluids. These occur in our environment as well as in our atmosphere and magnetosphere, and play a role in the sun's interaction with our planet. In most cases these phenomena involve turbulences, and thus are very challenging to understand and calculate. A sound knowledge is needed to tackle these problems. This work gives the basic information on turbulence in nature, comtaining the needed equations, notions and numerical simulations. The current state of our knowledge and future implications of MHD turbulence are outlined systematically. It is indispensable for all scientists engaged in research of our atmosphere and in space science.

TUrbulence modeling encounters mixed evaluation concerning its impor tance. In engineering flow, the Reynolds number is often very high, and the direct numerical simulation (DNS) based on the resolution of all spatial scales in a flow is beyond the capability of a computer available at present and in the foreseeable near future. The spatial scale of energetic parts of a turbulent flow is much larger than the energy dissipative counterpart, and they have large influence on the transport processes of momentum, heat, matters, etc. The primary subject of turbulence modeling is the proper es timate of these transport processes on the basis of a bold approximation to the energy-dissipation one. In the engineering community, the turbulence modeling is highly evaluated as a mathematical tool indispensable for the analysis of real-world turbulent flow. In the physics community, attention is paid to the study of small-scale components of turbulent flow linked with the energy-dissipation process, and much less interest is shown in the foregoing transport processes in real-world flow. This research tendency is closely related to the general belief that universal properties of turbulence can be found in small-scale phenomena. Such a study has really contributed much to the construction of statistical theoretical approaches to turbulence. The estrangement between the physics community and the turbulence modeling is further enhanced by the fact that the latter is founded on a weak theoretical basis, compared with the study of small-scale turbulence.

Monograph presents the newest results in the numerical modeling and computer simulation of turbulence.

A volume penalization method for the simulation of magnetohydrodynamic (MHD) flows in confined domains is presented. Incompressible resistive MHD equations are solved in 3D by means of a parallelized pseudo-spectral solver. The volume penalization technique is an immersed boundary method, characterized by a high flexibility in the choice of the geometry of the considered flow. In the present case, it allows the use of conditions different from periodic boundaries in a Fourier pseudo-spectral scheme. The numerical method is validated and its convergence is assessed for two- and three-dimensional hydrodynamical and MHD flows by comparing the numerical results with those of the literature or analytical solutions. Then, the spontaneous generation of kinetic and magnetic angular momentum is studied for confined 2D and 3D MHD flows. The influence of the Reynolds number and of the ratio of kinetic/magnetic energies is explored, as well as the differences induced by the boundary conditions. The fact that axisymmetric borders introduce a non-zero pressure term in the evolution equation of the angular momentum is essential to generate large values of the angular momentum. It is investigated whether this self-organization is exclusively observed in 2D flows by considering 3D MHD in the presence of a strong axial magnetic field. The last part is devoted to the simulation of a conducting fluid in a periodic cylinder with imposed axial and poloidal magnetic forcing, implying a resulting magnetic field. By varying the amplitude of the poloidal forcing, different dynamical states can be achieved. The effect of the Prandtl number on the threshold of the instabilities is then studied.

This book presents an introduction to, and modern account of, magnetohydrodynamic (MHD) turbulence, an active field both in general turbulence theory and in various areas of astrophysics. The book starts by introducing the MHD equations, certain useful approximations and the transition to turbulence. The second part of the book covers incompressible MHD turbulence, the macroscopic aspects connected with the different self-organization processes, the phenomenology of the turbulence spectra, two-point closure theory, and intermittency. The third considers two-dimensional turbulence and compressible (in particular, supersonic) turbulence. Because of the similarities in the theoretical approach, these chapters start with a brief account of the corresponding methods developed in hydrodynamic turbulence. The final part of the book is devoted to astrophysical applications: turbulence in the solar wind, in accretion disks, and in the interstellar medium. This book is suitable for graduate students and researchers working in turbulence theory, plasma physics and astrophysics.