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$\mathit{Re}\sim \mathit{Ha}^{2}$
for the amplitude of the Tayler destabilized flow is explained using a weakly nonlinear argument. We calculate a critical electrolyte height above which the Tayler instability is too weak to disrupt the electrolyte layer in a LMB. Applied to present day Mg-based batteries, this criterion shows that short circuits can occur only in very large batteries. Finally, preliminary results demonstrate the feasibility of direct numerical multiphase simulations of the Tayler instability in a model battery.
