Thursday 15 Oct 2020: 1st year PhD student presentations 1
Liam Watts and Azza Al Gatheem - University of Exeter
The scaling laws of flux expulsion in the kinematic and dynamic case - Liam Watts
Abstract: Flux expulsion is a process within the sun that allows magnetic flux to be transported. If we consider a convective eddy and impose a weak magnetic field onto it, the eddy will advect the field, causing spiral wind up until the gradients between adjacent field lines are so large that magnetic reconnection occurs causing flux to be expelled from the central region of the eddy. We are considering two main cases for flux expulsion: the kinematic case, where the field is sufficiently weak that it has no effect on the flow and the dynamic case, where the magnetic field is sufficiently strong that it will cause a back-reaction onto the flow. We also find that the time-scale associated with flux expulsion follows Moffatt and Kamkar's scaling law only holds for certain flows and there are potentially new scaling laws associated with more complex flows.
Jets and Instabilities in Forced MHD Flows - Azza Al Gatheem
It is known that forced fluid flows can be unstable to the formation of large-scale jet motions. These instabilities can occur in the presence of the β-effect, called ”zonostrophic instability”, and has implications for observed geophysical and astrophysical systems. However, in astrophysical bodies such as the Sun, magnetic fields are also present, and how these field change the stability is still not understood. We consider Kolmogorov flow with magnetic field. Our initial results focus on the β=0 regime, where the hydrodynamic flow is unstable when R_c= 1/ε_c=√2. We studied the MHD case for both vertical and horizontal fields and determined the stability. In the case of the vertical field, we are found the adding magnetic field suppresses the original instability. By comparison, two different types of instability appear in the case of the horizontal field, which produces a more complicated structure of the eigenfunction than the vertical field because of the flow advecting field lines. The results will be relevant to understanding the effect of magnetic field on the stability of flows in the solar tachocline.