Reflection of Alfvén wave at the boundary

Alfvén wave is a type of magnetohydrodynamic wave propagating in conducting fluids and plasma. The wave relies on the Lorentz force generated by the motion of the flow normal to a background magnetic field as the restoring force. For more details, refer to the post Alfvén wave in the Notes section.

How does Alfvén exactly behave at the interface between two media? Ferraro (1954) has studied this problem long ago for the interface between two ideal (i.e. diffusionless) fluids. His derivations seem straightforward, but his treating the electromagnetic fields to be continuous across the interface seems questionable. The diffusionless case is also of little applicational concern.

More recent developments on this topic, especially in the field of geophysical fluid dynamics, are attributed to Schaeffer, Jault et al (2012) as well as Schaeffer and Jault (2016). In their papers, they elegantly treated the interface between a (viscous and magnetically) diffusive fluid and a solid wall. They point out that the reflection behaviour depends on (i) the magnetic Prandtl number, and (ii) the conductivity of the wall. However, they only treat the 1-D case.

The aim of the current project is to give a comprehensive treatment of the Alfvén wave at fluid-solid interface, in full 3-D geometry. I want to identify the ingredients that are active in general 3-D incoming waves. As an example in GFD, I hope to understand how the torsional waves would behave at the core-mantle boundary. Current development is documented in the main formulation document (also top of this page).