Nature of branching in electrohydrodynamic instability

An electric field imposed on a bilayer of fluids that are stably stratified in the presence of gravity leads to an instability manifested by interfacial deflections. For the case of a perfect conductor underlying a perfect dielectric, an analytical expression obtained from weak nonlinear analysis shows that sinusoidal deflections can only lead to subcritical breakup. While this expression indicates that there is a transition wave number below which supercritical saturation ought to occur, it can be shown that such wave numbers cannot be geometrically accessed, thus precluding any supercritical saturation to steady waves.

Automated summary

An electric field applied to a bilayer of fluids with stable stratification and gravity can cause an instability resulting in interfacial deflections. In the case of a perfect conductor under a perfect dielectric, weak nonlinear analysis shows that sinusoidal deflections will only lead to subcritical breakup, as geometrically inaccessible wave numbers prevent supercritical saturation.