Magnetic Field Generation and Critical Reynolds and Prandtl numbers
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
Magnetic field generation, called dynamo mechanism, is one of the outstanding problems in physics and astrophysics. Recent experiments and numerical simulations indicate that magnetic field generation takes place in magnetohydrodynamic plasmas for a range of magnetic Reynolds number and Prandtl number. We analytically study dynamo problem using low-dimensional models. We start with the large-scale velocity and magnetic field modes, and construct nonlinear models keeping the interactions among these modes. The resulting equations are a low dimensional set of ordinary differential equations that can be analytically solved. We find that the magnetic field grows for magnetic Reynolds number greater than a critical magnetic field. The critical magnetic Reynolds number depends on the Prandtl number. Different models for high and low Prandtl number are proposed. These results are in general agreement with present experiments and numerical simulations.
In order to test the ability of this approach to describe the existence of dynamo, the analytical solution of the low-dimensional model is compared with the numerical solution of the full nonlinear MHD equations obtained using a pseudo-spectral code with a forcing acting on the large-scale modes. The numerical simulations show a reasonable agreement with the analytic solutions.
Our results indicate that large-scale velocity and magnetic fields are important for dynamo action. This supports the idea that low-dimensional models based on these variables are very useful for understanding the dynamics of dynamo.