event
Thursday 03 Nov 2011: Maths seminar - Exploiting symmetries in dynamo simulations
Sam Jones - University of Exeter
Harrison 203 15:00-16:00
Dynamo theory is concerned with how the motion of an electrically conducting fluid can generate and maintain a magnetic field.
Derived from Maxwell?s equations, the magnetic induction equation is the magnetic equivalent of the Navier-Stokes equation and describes the evolution of a magnetic field through its interaction with a velocity field. An important parameter, the magnetic Reynolds number (Rm), controls the scale of advection to diffusion in the induction equation.
Of interest in dynamo theory is whether certain flows can maintain a magnetic field for increasing values of Rm. The ABC flow is a family of flows which are highly helical and also have a high degree of rotational symmetry. These inherent symmetries are exploited to reduce the domain required to simulate the full dynamo problem, thus saving on computation time and allowing larger values of Rm to be simulated for. In doing so, the field has to be deconstructed into its five fundamental symmetry classes (I-V), allowing the structure of the dynamos to be studied with greater detail.
Results of simulations for Rm up to O(103) will be discussed, as well as an alternative method of solving the induction equation.
