  Magnetohydrodynamically induced interface instability in liquid metal
batteries is analyzed. The batteries are represented by a simplified system in
the form of a rectangular cell, in which strong vertical electric current flows
through three horizontal layers: the layer of a heavy metal at the bottom, the
layer of a light metal at the top, and the layer of electrolyte in the middle.
A new two-dimensional nonlinear model based on the conservative shallow water
approximation is derived and utilized in a numerical study. It is found that in
the case of small density difference between the electrolyte and one of the
metals, the instability closely resembles the rolling pad instability observed
earlier in the aluminum reduction cells. When the two electrolyte-metal density
differences are comparable, the dynamics of unstable systems is more complex
and characterized by interaction between two nearly symmetric or antisymmetric
interfacial waves.
